Dan Coman, George Marinescu
We prove the convergence of the normalized Fubini-Study measures and the logarithms of the Bergman kernels of various Bergman spaces of holomorphic and weakly holomorphic sections associated to a singular Hermitian holomorphic line bundle on an algebraic curve. Using this, we study the asymptotic distribution of the zeros of random sequences of sections in these spaces.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
We establish an equidistribution theorem for the zeros of random holomorphic sections of high powers of a positive holomorphic line bundle. The equidistribution is associated with a family of singular moderate measures. We also give a convergence speed for the equidistribution.
Given several sequences of Hermitian holomorphic line bundles $\{(L_{kp}, h_{kp})\}_{p=1}^{\infty}$, we establish the distribution of common zeros of random holomorphic sections of $L_{kp}$ with respect to singular measures. We also study the dimension growth for a sequence of pseudo-effective line bundles.
We establish an equidistribution theorem for the common zeros of random sections of high powers of several singular Hermitian big line bundles associated to moderate measures.
We establish the equidistribution of zeros of random holomorphic sections of powers of a semipositive singular Hermitian line bundle, with an estimate of the convergence speed.
Equidistribution of Fekete points on complex manifolds
证明了复平面上紧子集上Fekete点的等分布定理的多元形式，解决了复位势论中的一个著名猜想.所得结果是紧复流形上给定全纯线丛的Fekete点的一般等分布定理的一个特例。证明建立在我们最近的工作“容量和加权卷线丛“。
Equidistribution towards the Green current for holomorphic maps
设f是射影空间的不可逆全纯自同态，f^n是它的n阶群.我们证明了当n趋于无穷大时，一个一般（在Zerkiki意义下）超曲面的f^n的拉回，经过适当的规范化，收敛到与f相关的格林流。对于正闭（1，1）-电流的拉回，我们也给出了类似的结果。
We study the equidistribution of Fekete points in a compact complex manifold. These are extremal point configurations defined through sections of powers of a positive line bundle. Their equidistribution is a known result. The novelty of our approach is that we relate them to the problem of sampling and interpolation on line bundles, which allows us to estimate the equidistribution of the Fekete points quantitatively. In particular we estimate the Kantorovich-Wasserstein distance of the Fekete points to its limiting measure. The sampling and interpolation arrays on line bundles are a subject of…
Let K be the closure of a bounded open set with smooth boundary in C^n. A Fekete configuration of order p for K is a finite subset of K maximizing the Vandermonde determinant associated with polynomials of degree at most p. A recent theorem by Berman, Boucksom and Witt Nystrom implies that Fekete configurations for K are asymptotically equidistributed with respect to a canonical equilibrium measure, as p tends to infinite. We give here an explicit estimate for the speed of convergence. The result also holds in a general setting of Fekete points associated with an ample line bundle over a proje…
Equidistribution of graphs of holomorphic correspondences
研究紧黎曼曲面上的全纯自对应，在动力学度不相等或非弱模条件下，证明迭代图的指数快速等分布。
In this paper, we discuss the equidistribution phenomena for holomorphic endomorphisms over $\mathbb{P}^k$ in the case of bidegree $(p,p)$ with $1<p<k$. We prove that if $f:\mathbb{P}^k\to\mathbb{P}^k$ is a holomorphic endomorphism of degree $d\geq 2$ and $T^p$ denotes the Green $(p,p)$-current associated with $f$, then there exists a proper invariant analytic subset $E$ for $f$ such that $d^{-pn}(f^n)^*(S)\to T^p$ exponentially fast in the current sense for every positive closed $(p,p)$-current $S$ of mass 1 such that $S$ is smooth on $E$.
Equidistribution for Random Polynomials and Systems of Random Holomorphic Sections
本文研究随机全纯截面和随机多项式零点的等分布性，通过非正交基和广义概率测度证明了更一般的等分布结果，扩展了Bernstein-Markov测度的概念并给出了全局等分布、方差估计和分布定理。
Equidistribution of saddle periodic points for automorphisms on compact Kähler manifolds
本文证明了紧致Kähler流形上具有简单上同调作用的全纯自同构的鞍型周期点关于平衡测度等分布，并推广到正拓扑熵的Kähler曲面情形。
We study the asymptotics of Fubini-Study currents and zeros of random holomorphic sections associated to a sequence of singular Hermitian line bundles on a compact normal Kaehler complex space.
Equidistribution of zeros of random holomorphic sections
研究随机全纯截面在高次正线丛上零点的渐近分布，证明了在正则紧致集上正交多项式线性组合的归一化零测度几乎必然趋于该集的均衡测度。
We study the distribution of the common zero sets of $m$-tuples of holomorphic sections of powers of $m$ singular Hermitian pseudo-effective line bundles on a compact Kähler manifold. As an application, we obtain sufficient conditions which ensure that the wedge product of the curvature currents of these line bundles can be approximated by analytic cycles.
We show that normalized currents of integration along the common zeros of random $m$-tuples of sections of powers of $m$ singular Hermitian big line bundles on a compact Kähler manifold distribute asymptotically to the wedge product of the curvature currents of the metrics. If the Hermitian metrics are Hölder with singularities we also estimate the speed of convergence.
Let f be a non-invertible holomorphic endomorphism of P^k. For a hypersurface H of P^k, generic in the Zariski sense, we give an explicit speed of convergence of f^{-n}(H) towards the dynamical Green (1,1)-current of f.
On holomorphic Banach vector bundles over Banach spaces
我们显示，例如，在希尔伯特空间的伪凸开子集上的全纯Banach向量丛是全纯平凡的，如果它是连续平凡的。并给出了一些应用实例。
We establish an approximation of the activity current $T_c$ in the parameter space of a holomorphic family $f$ of rational functions having a marked critical point $c$ by parameters for which $c$ is periodic under $f$, i.e., is a superattracting periodic point. This partly generalizes a Dujardin--Favre theorem for rational functions having preperiodic points, and refines a Bassanelli--Berteloot theorem on a similar approximation of the bifurcation current $T_f$ of the holomorphic family $f$. The proof is based on a dynamical counterpart of this approximation.
Extension of holomorphic bundles to the disc (and Serre's Problem on Stein bundles)
我们用一种非常简单的技巧证明了如何将一些以C^2为中心的全纯丛和以C中的开集为基的全纯丛扩张为黎曼球面上的丛。特别是，它适用于由斯柯达和Demailly构造的非Stein丛的例子。它给出了一个C上的例子，具有多项式转换自同构。
Given a sequence of positive Hermitian holomorphic line bundles $(L_p,h_p)$ on a Kähler manifold $X$, we establish the asymptotic expansion of the Bergman kernel of the space of global holomorphic sections of $L_p$, under a natural convergence assumption on the sequence of curvatures $c_1(L_p,h_p)$. We then apply this to study the asymptotic distribution of common zeros of random sequences of $m$-tuples of sections of $L_p$ as $p\to\infty$.
On the extension of twisted holomorphic sections of singular hermitian line bundles
证明了几乎Stein流形上奇异厄米线丛的扭曲全纯截面的一个尖锐的Ohsawa-Takegoshi-Manivel型扩张结果。作为推论，我们建立了射影流形上奇异厄米线丛的多扭全纯截面的一些推广结果。
A splitting theorem for holomorphic Banach bundles
本文的出发点是Grothendieck分裂定理。在1960年代，Gohberg将其推广到一类Banach丛。我们考虑一个紧致复流形$X$和一个全纯Banach丛$E \to X$，这是一个紧扰动的平凡丛的一个意义上最近推出的Lempert。我们证明了$E$分裂成有限秩丛和平凡丛的和，条件是$H^{1}(X, Ø)=0$。
We establish triviality of some holomorphic Banach vector bundles on the maximal ideal space of the Banach algebra of bounded holomorphic functions on the unit disk with pointwise multiplication and supremum norm. We apply the result to the study of the Sz.-Nagy operator corona problem.
We obtain the Bogomolov-Sommese type vanishing theorem involving multiplier ideal sheaves for big line bundles. We define a dual Nakano semi-positivity of singular Hermitian metrics with L2-estimates and prove the vanishing theorem which is a generalization of the Bogomolov-Sommese type vanishing theorem to holomorphic vector bundles.
We study ellipticity properties of complements of compact subsets of Stein manifolds.
On the dynamics of codimension one holomorphic foliations with ample normal bundle
本文研究了法丛充足的余维1叶理的叶到奇点的积累问题，重点讨论了Levi-平坦超曲面的不存在性。
In this paper, we study the regular quantizations of Kähler manifolds by using the first two coefficients of Bergman function expansions. Firstly, we obtain sufficient and necessary conditions for certain Hermitian holomorphic vector bundles and their ball subbundles to be regular quantizations. Secondly, we obtain that some projective bundles over the Fano manifolds $M$ admit regular quantizations if and only if $M$ are biholomorphically isomorphism to the complex projective spaces. Finally, we obtain the balanced metrics on certain Hermitian holomorphic vector bundles and their ball subbundl…
On the cohomology groups of holomorphic Banach bundles
考虑紧致复流形$M$，引入了$M$上的两个全纯Banach丛$E,F$相互紧扰动的概念.给定两个这样的丛，我们表明，如果上同调群$H^q(M,E)$是有限维的，那么上同调群$H^q(M,F)$也是有限维的;以及在相同的精神更精确的结果。
Let f be a non-invertible holomorphic endomorphism of the complex projective space P^k and f^n its iterate of order n. Let V be an algebraic subvariety of P^k which is generic in the Zariski sense. We give here a survey on the asymptotic equidistribution of the sequence $f^{-n}(V)$ when n goes to infinity.
Holomorphic extension in holomorphic fiber bundles with (1,0)-compactifiable fiber
本文利用Leray谱序列、Čech论证和Künneth公式等工具，研究具有(1,0)-可紧化纤维的全纯纤维丛全空间上的Hartogs现象，并得到相应的消失性结果。
In 1985 Diederich and Ohsawa proved that every disc bundle over a compact Kähler manifold is weakly 1-complete. In this paper, under certain conditions we generalize this result to the case of fiber bundles over compact Kähler manifolds whose fibers are bounded symmetric domains. Moreover if the bundle is obtained by the diagonal action on the product of irreducible bounded symmetric domains, we show that it is hyperconvex.
Approximation and extension of Hermitian metrics on holomorphic vector bundles over Stein manifolds
本文证明了Stein流形上全纯向量丛中满足Griffiths或Nakano意义下负曲率的奇异Hermitian度量可由光滑度量序列逼近，且限制在子流形上的此类光滑度量可延拓至整个丛并保持相同曲率负性。
Holomorphic fiber bundle with Stein base and Stein fibers
本文证明了：若$Π: X\to Ω$是满射全纯映射，$Ω$是Stein空间，$X$是维数为$n\geq 3,$的复流形，且对每个$x\in Ω$，存在开邻域$U$使得$Π^{-1}(U)$是Stein，则$X$是Stein
In this paper we review the use of techniques of positive currents for the study of parameter spaces of one-dimensional holomorphic dynamical systems (rational mappings on P^1 or subgroups of the Moebius group PSL(2,C)). The topics covered include: the construction of bifurcation currents and the characterization of their supports, the equidistribution properties of dynamically defined subvarieties on parameter space.
Oka's principle for holomorphic fiber bundles with sprays
我们给出了M的下列定理的证明。Gromov（Oka's principle for holomorphic sections of elliptical bundles，J. Amer. Math. Soc.，2（1989），851-897）。设Z是Stein流形上的全纯纤维丛。若Z的纤维包含一个控制全纯喷，则Z的整体全纯截面空间包含在连续截面空间中是弱同伦等价。在经典情况下，当纤维是一个复李群或齐性空间时，H. Grauert（Math. Ann.，135（1958），263- 273）。关于这方面的进一步结果，请参见math.CV/0101040、math.CV/0101040、math.CV/0101034、math.CV/0101238、math.CV/0107039、math.CV/0110201。
Equidistribution speed for endomorphisms of projective spaces
设f是复射影空间P^k的一个不可逆全纯自同态，f^n是它的n阶子空间，μ是f的平衡测度.我们在下面的已知结果中估计收敛速度。如果a是P^k中的Zapriki泛点，则在f^n下均匀分布在a的原像上的概率测度在n趋于无穷大时收敛于μ。
We construct a pair (E ,F), where E is a holomorphic vector bundle over a compact Riemann surface and F a holomorphic subbundle of E, such that both F and E/F admit holomorphic connections, but E does not.
A Remark on Optimal $L^2$ extension theorem for holomorphic vector bundles
本文在弱拟凸 Kähler 流形上建立了带光滑 Hermite 度量的全纯向量丛在连续增益条件下的最优 $L^2$ 延拓定理，统一了 Guan-Zhou 与 Zhou-Zhu 的已有结果。
Consider a domain $\varOmega$ in $\mathbb{C}^n$ with $n\geqslant 2$ and a compact subset $K\subset\varOmega$ such that $\varOmega\backslash K$ is connected. We address the problem whether a holomorphic line bundle defined on $\varOmega\backslash K$ extends to $\varOmega$. In 2013, Fornæss, Sibony and Wold gave a positive answer in dimension $n\geqslant 3$, when $\varOmega$ is pseudoconvex and $K$ is a sublevel set of a strongly plurisubharmonic exhaustion function. However, for $K$ of general shape, we construct counterexamples in any dimension $n\geqslant 2$. The key is a certain gluing lemma…
We consider N-tensor powers of a positive Hermitian line bundle L over a non-compact complex manifold X. In the compact case, B. Shiffman and S. Zelditch proved that the zeros of random sections become asymptotically uniformly distributed with respect to the natural measure coming from the curvature of L, as N tends to infinity. Under certain boundedness assumptions on the curvature of the canonical line bundle of X and on the Chern form of L we prove a non-compact version of this result. We give various applications, including the limiting distribution of zeros of cusp forms with respect to t…
Given a compact complex manifold $M$, we investigate the holomorphic vector bundles $E$ on $M$ such that $φ^* E$ is trivial for some surjective holomorphic map $φ$, to $M$, from some compact complex manifold. We prove that these are exactly those holomorphic vector bundles that admit a flat holomorphic connection with finite monodromy homomorphism. A similar result is proved for holomorphic principal $G$-bundles, where $G$ is a connected reductive complex affine algebraic group.
Holomorphic Factorization of Vector Bundle Automorphisms
该研究在复几何领域证明了Stein空间上秩2向量丛的零伦特殊全纯自同构可分解为有限个幂幺自同构或指数映射的乘积，推进了全纯向量丛自同构的结构研究。
We prove that actions of complex reductive Lie groups on a holomorphic vector bundle over a complex compact manifold are locally extendable to its local moduli space.
We characterize operator-theoretic properties (boundedness, compactness, and Schatten class membership) of Toeplitz operators with positive measure symbols on Bergman spaces of holomorphic hermitian line bundles over Kähler Cartan-Hadamard manifolds in terms of geometric or operator-theoretic properties of measures.
In the present paper, we study the properties of singular Nakano positivity of singular hermitian metrics on holomorphic vector bundles, and establish an optimal $L^2$ extension theorem for holomorphic vector bundles with singular hermitian metrics on weakly pseudoconvex Kähler manifolds. As applications, we give a necessary condition for the holding of the equality in optimal $L^2$ extension theorem, and present singular hermitian holomorphic vector bundle versions of some $L^2$ extension theorems with optimal estimate.
Holomorphic vector bundles on primary Kodaira surfaces
在非代数曲面上的拓扑复向量丛中，哪些是全纯结构，一般是未知的。我们解决了这个问题的主要Kodaira曲面的Kani曲线的亏格2椭圆微分的结果。某些相应的模空间将是光滑紧的和全纯辛的。
Holomorphic Jet Bundles
计算了全纯射束在射影曲线和射影曲面上的陈数公式。这些公式用于证明某些一般类型的极小曲面（特别是射影3-空间中至少5次的一般超曲面）在复双曲几何意义下是双曲的。
We prove an extension theorem for roots and logarithms of holomorphic line bundles across strictly pseudoconcave boundaries: they extend in all cases except one, when dimension and Morse index of a critical point is two. In that case we give an explicit description of obstructions to the extension.
Holomorphic rank-2 vector bundles on non-Kahler elliptic surfaces
光滑紧致复曲面上的向量丛的存在性问题在于确定哪些拓扑复向量丛允许全纯结构。对于射影曲面，Schwarzenberger证明了拓扑复向量丛具有全纯（代数）结构当且仅当它的第一个陈类属于曲面的Neron-Severi群。相反，对于非射影曲面，存在性问题只有一个必要条件（向量丛的判别式必须是正的），问题的困难在于缺乏构造非滤向量丛的一般方法.本文通过给出非K\”ahler椭圆曲面上全纯秩为2的向量丛存在的充要条件，封闭了秩为2情形下的存在性问题.
We study a tower of normal coverings over a compact Kähler manifold with holomorphic line bundles. When the line bundle is sufficiently positive, we obtain an effective estimate, which implies the Bergman stability. As a consequence, we deduce the equidistribution for zero currents of random holomorphic sections. Furthermore, we obtain a variance estimate for those random zero currents, which yields the almost sure convergence under some geometric condition.
In this paper we study holomorphic vector bundles with singular Hermitian metrics whose curvature are Hermitian matrix currents. We obtain an extension theorem for holomorphic jet sections of nef holomorphic vector bundle on compact Kähler manifolds. Using it we prove that Fano manifolds with strong Griffiths nef tangent bundles are rational homogeneous spaces.
We generalize a construction of Hitchin to prove that, given any compact Kähler manifold $M$ with positive holomorphic sectional curvature and any holomorphic vector bundle $E$ over $M$, the projectivized vector bundle ${\mathbb P}(E)$ admits a Kähler metric with positive holomorphic sectional curvature.
In this paper we provide sufficient conditions for maps of vector bundles on smooth projective varieties to be uniquely determined by their degeneracy schemes. We then specialize to holomorphic distributions and foliations. In particular, we provide sufficient conditions for distributions of arbitrary rank on projective spaces to be uniquely determined by their singular schemes.
Generalized Demailly-Semple jet bundles and holomorphic mappings into complex manifolds
受Green-Griffiths猜想的启发，我们研究了从$\C^p$到复流形的极大秩全纯映射.当使用$p>1$时，原则上这些图应该比整个曲线更易处理。我们扩展到这个设置的喷射束技术介绍了森普尔，绿色格里菲斯和Demailly。我们的主要应用是证明了从$\C^2$到$\bP^4$中非常一般次数的$d$超曲面的极大秩全纯映射的不存在性，只要$d\geq 93.$
We study critical points of holomorphic sections of $\ocal(m)$ on $\CP^n$. For quadrics, we give a complete discription of their critical points. When $n=1$, we prove a spherical Gauss-Lucas theorem. For general situation, we prove that a general section has all its critical points isolated and non-degenerate.
The loop space $L\mathbb{P}_1$ of the Riemann sphere consisting of all $C^k$ or Sobolev $W^{k,p}$ maps from the circle $S^1$ to $\mathbb{P}_1$ is an infinite dimensional complex manifold. The loop group $LPGL(2,\mathbb{C})$ acts on $L\mathbb{P}_1$ . We prove that the group of $LPGL(2,\mathbb{C})$ invariant holomorphic line bundles on $L\mathbb{P}_1$ is isomorphic to an infinite dimensional Lie group. Further, we prove that the space of holomorphic sections of these bundles is finite dimensional, and compute the dimension for a generic bundle.
Holomorphic approximation for Hamiltonian diffeomorphism groups via the Symplectic Density Property
该研究证明全纯灵活Stein流形的余切丛具有辛密度性质，进而推导得出实余切丛的哈密顿微分同胚可由复化余切丛的复辛自同构实现Carleman意义下的全纯逼近。
Holomorphic vector bundles on non-algebraic surfaces
非代数曲面上向量丛上的全纯结构的存在性问题一般仍是一个未解决的问题。我们解决了这个问题的情况下，秩2向量丛在K3表面和任意秩的向量丛在所有已知的曲面类VII。我们的方法是基于Donaldson理论和形变理论的，可以用来解决更多类非代数曲面上全纯向量丛的存在性问题。
We investigate singular Hermitian metrics on vector bundles, especially strictly Griffiths positive ones. $L^2$ esitimates and vanishing theorems usually require an assumption that vector bundles are Nakano positive. However there is no general definition of the Nakano positivity in singular settings. In this paper, we show various $L^2$ estimates and vanishing theromes by assuming that the vector bundle is strictly Griffiths positive and the base manifold is projective.
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。