Haibao Duan, Banghe Li
Let M be the blow--up of a manifold M along a submanifold X. In this paper we present closed formulae for the integral cohomology and the total Chern class of M. As applications we compute the cohomology of the varieties of complete conics and complete quadrices in 3--space, and justify two enumerative results due to Schubert.
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
The quantum cohomology of blow-ups of P^2 and enumerative geometry
我们计算了在r个一般点上炸开的射影平面的Gromov-Witten不变量。这些由r+1初始值的结合性确定。应用程序给出了合理的平面曲线的计数与规定的重数在固定的一般点。我们表明，如果至少有一个规定的多重数是1或2的数字是枚举的。特别地，所有r<=8的不变量（Del Pezzo情况）都是枚举的。
We extend the formula for the Chern classes of blow-ups of algebraic varieties due to Porteous and Lascu-Scott, and of symplectic and complex manifolds due to Geiges and Pasquotto, to the blow-ups of almost complex manifolds. Our approach is based on a concrete partition for the tangent bundle of a blow-up. The use of topological K-theory of vector bundles simplifies the classical approaches.
We prove that if a symplectic 4-manifold $X$ becomes a rational 4-manifold after applying rational blow-down surgery, then the symplectic 4-manifold $X$ is originally rational. That is, a symplectic rational blow-up of a rational symplectic $4$-manifold is again rational. As an application we show that a degeneration of a family of smooth rational complex surfaces is a rational surface if the degeneration has at most quotient surface singularities, which generalizes slightly a classical result of [Bădescu, 1986] in algebraic geometry under a mild additional condition.
We propose another proof of the geometric class field theory for curves by considering blow-ups of symmetric products of curves.
The purely log terminal blow-ups of three-dimensional terminal toric singularities are described.
We consider the problem to determine which blow-ups along subvarieties in products of two projective spaces are log Fano. By describing the nef cones of such blow-ups with special centers, we give a partial classification result. For each example, explicit boundary divisors are also given.
Blow-ups of three-dimensional terminal singularities: cA case
在cA点上具有最小差异的除数被分类
We answer a question of Keel: How much can one improve a non-toroidal ideal sheaf by a sequence of toroidal blow-ups? Version2: Corollary 5 was proved earlier by Tevelev and Ulirsch.
In this paper we determine which blow-ups $X$ of $\mathbb{P}^n$ at general points are log Fano, that is, when there exists an effective $\mathbb{Q}$-divisor $Δ$ such that $-(K_X+Δ)$ is ample and the pair $(X,Δ)$ is klt. For these blow-ups, we produce explicit boundary divisors $Δ$ making $X$ log Fano.
Higher Nash blow-ups and Nobile theorem
本文研究T. Yasuda提出的高阶纳什爆破及经典诺比尔定理的高阶版本，给出分次情形下高阶诺比尔定理的无特征证明，以及特征零情形下次二阶纳什爆破的证明。
Logarithmic resolution of singularities in characteristic 0 using weighted blow-ups
本文研究特征零域上的奇点消解问题，核心方法是使用加权爆破，构造出例外因子呈简单正常交叉的对数消解。
Gromov-Witten invariants of blow-ups
在本文的第一部分中，我们给出了一个显式算法来计算（亏格为零）Gromov-Witten不变量的爆破的任意凸射影簇在某些点，如果一个人知道原簇的Gromov-Witten不变量。在第二部分中，我们专门研究了P^r的爆破，并证明了这些爆破的许多不变量可以解释为P^r上的有理曲线的个数，这些曲线在爆破点处具有指定的全局重数或切方向。我们给出了各种数值例子，包括一个新的简单的方法来确定著名的多重性d^{-3}的d-折叠覆盖的有理曲线的五次三倍，并作为一个展望，两个例子的爆破沿子品种，其Gromov-Witten不变量导致经典的多割线公式。
We use degeneration formula to study the change of stable pair invariants of 3-folds under blow-ups and obtain some closed blow-up formulae. Related results on Donaldson-Thomas invariants are also discussed. Our results give positive evidence for GW/DT/P correspondence, and also give partial correspondence for varieties not necessarily toric or complete intersections.
On purely log terminal blow-ups
本文证明了Kawamata对数终端奇点的纯对数终端blow-up的存在性，并利用plt blow-up的例外因子得到了奇点弱例外的判据.
Positivity of line bundles on general blow ups of Hirzebruch surfaces
本文研究Hirzebruch曲面一般爆胀上线丛的正性，针对丰富性、整体生成性、非常丰富性和k-非常丰富性分别给出充分的数值条件。
On the quantum cohomology of blow-ups of projective spaces along linear subspaces
给出了射影空间沿线性子空间爆破的量子上同调环的生成元和关系式。
Inverting log blow-ups in log geometry
本文通过局部逆构对数胀开引入可除对数空间范畴，证明对数光滑可除对数空间的闭浸入存在胀开，为对数概形母题六函子形式化提供基础。
This paper is a revision of the author's old preprint "Exactness, integrality, and log modifications". We will prove that any quasi-compact morphism of fs log schemes can be modified locally on the base to an integral morphism by base change by fs log blow-ups.
In this paper we study the pseudoeffective cones of blow-ups of Grassmannians at sets of points. For small numbers of points, the cones are often spanned by proper transforms of Schubert classes. In some special cases, we provide sharp bounds for when the Schubert classes fail to span and we describe the resulting geometry.
We use a family of algebraic foliations given by A. Lins Neto to provide new evidences to a conjecture, related to the Harbourne-Hirschowitz's one and implying the Nagata's conjecture, which concerns the structure of the Mori cone of blow-ups of $\mathbb{P}^2$ at very general points.
We study k-very ampleness of line bundles on blow-ups of hyperelliptic surfaces at r very general points. We obtain a numerical condition on the number of points for which a line bundle on the blow-up of a hyperelliptic surface at these r points gives an embedding of order k.
Numerical invariants for bundles on blow-ups
我们提出了一个有效的方法来计算爆破曲面上秩二丛的数值不变量。研究了爆破平面上例外因子分裂为O（j）+O（-j）的丛的模空间M_j.我们利用数值不变量给出了M_j的一个拓扑分解。
Cones of effective cycles on blow ups of projective spaces along rational curves
该研究针对射影空间沿光滑有理曲线的爆破上的有效闭链锥问题，明确确定了有理正规曲线爆破上的除子、一维及二维闭链锥，低维下结果更优，其割线簇消解几何为核心，有效闭链计算具独立价值。
Virtual Cartier divisors and blow-ups
本文基于“虚拟有效Cartier除子”概念证明正则浸入子概形胀开的泛性质，并在导出代数几何中构造拟光滑闭浸入的胀开，推进了胀开相关理论研究。
In this paper we classify weak Fano varieties that can be obtained by blowing-up general points in prime Fano varieties. We also classify spherical blow-ups of Grassmannians in general points, and we compute their effective cone. These blow-ups are, in particular, Mori dream spaces. Furthermore, we compute the stable base locus decomposition of the blow-up of a Grassmannian in one point, and we show how it is determined by linear systems of hyperplanes containing the osculating spaces of the Grassmannian at the blown-up point, and by the rational normal curves in the Grassmannian passing throu…
We establish a blow-up formula for Hodge cohomology of locally free sheaves on smooth proper varieties over an algebraically closed field of positive characteristic. For this, we introduce a notion of relative Hodge sheaves and study their behavior under blow-ups along smooth centers. In particular, as an application, we study the blow-up invariance of the $E_2$-degeneracy of the Hochschild--Kostant--Rosenberg spectral sequence for smooth proper varieties.
The aim of this note is to investigate the relation between two types of non-singular projective varieties of Picard rank 2, namely the Projective bundles over Projective spaces and certain Blow-up of Projective spaces.
Fano manifolds and blow-ups of low-dimensional subvarieties
本文研究伪指数大于1、维数大于5的Fano流形，它是光滑簇沿维数等于流形伪指数的光滑中心的Blow-ups。我们得到了这些流形的可能的曲线锥的分类，我们证明了只有一个这样的流形没有纤维型初等收缩。
The aim of this paper is twofold. Firstly, we determine which blow-ups of products of projective spaces at general points are varieties of Fano type, and give boundary divisors making these spaces log Fano pairs. Secondly, we describe generators of the Cox rings of some cases.
Sequences of point blow-ups over perfect fields from a combinatorial point of view
本文用加权有向图和 d 元相交形式刻画完美域上的点爆发序列及其复合，并通过相容划分证明二者在组合与代数等价类之间均存在双射。
In this paper we classify all the compactifications of affine homology $3$-cells into the blow-ups of the projective $3$-space along smooth curves such that the log canonical divisors are linearly trivial. As a result, we prove that each embedded affine $3$-fold is isomorphic to the affine $3$-space except one example.
Let X be a compact toric surface. There exists a sequence of torus equivariant blow-ups of X such that the blown-up toric surface obtained admits a cscK metric.
Anti-flips of the blow-ups of the projective spaces at torus invariant points
本文通过反翻转显式构造光滑环面法诺簇，使其同构于射影空间在余维一环面不变点处的爆破。
In order to count the number of smooth cubic hypersurfaces tangent to a prescribed number of lines and passing through a given number of points, we construct a compactification of their moduli space. We term the latter a $1$--\textit{complete variety of cubic hypersurfaces} in analogy to the space of complete quadrics. Paolo Aluffi explored the case of plane cubic curves. Starting from his work, we construct such a space in arbitrary dimension by a sequence of five blow-ups. The counting problem is then reduced to the computation of five Chern classes, climbing the sequence of blow-ups. Comput…
In order to study wall crossing formula of Donaldson type invariants on the blown-up plane, Nakajima-Yoshioka constructed a sequence of blow-up/blow-down diagrams connecting the moduli space of torsion free framed sheaves on projective plane, and that on its blow-up. In this paper, we prove that Nakajima-Yoshioka's diagram realizes the minimal model program. Furthermore, we obtain a fully-faithful embedding between the derived categories of these moduli spaces.
Given a sequence of point blow-ups of smooth n-dimensional projective varieties $Z_{i}$ defined over an algebraically closed field k, $Z_{s}\rightarrow Z_{s-1}\rightarrow ...\rightarrow Z_{1}\rightarrow Z_{0}$, we give two presentations of the Chow ring of its sky $A^{\bullet}(Z_{s})$. The first one using the classes of the total transforms of the exceptional components as generators and the second one using the classes of the strict transforms ones. We prove that the skies of two sequences of point blow-ups of the same length have isomorphic Chow rings. Finally we give a characterization of f…
Polarized cylinders on blow-ups of weighted projective planes
研究加权射影平面吹胀得到的有理表面中的偏极化圆柱，分析其作为加权超曲面或拟光滑完全交集的自然出现形式。
We study the projective spectrum of the Rees algebra of a module, and characterize it by a universal property. As applications, we give descriptions of universal flatifications of modules and of birational projective morphisms.
Resolving plane curves using stack-theoretic blow-ups
本文针对正特征域上曲线奇点消解中因加权爆破导致切空间维度增加而难以进行归纳的问题，提出利用规范构造的多重加权爆破方法克服了这一挑战。
Bigness of tangent bundles of blow-ups of ruled surfaces
研究直纹曲面\(S = \mathbb{P}_C(\mathcal{E})\)在点爆破下切丛丰沛性的保持情况，通过第一塞格雷不变量\(s_1(\mathcal{E})\)给出爆破点数的精确界。
Raphaël Rouquier introduced an invariant of triangulated categories which is known as Rouquier dimension. Orlov conjectured that for any smooth quasi-projective variety $X$ the Rouquier dimension of $D^b_{\mathrm{coh}}(X)$ is equal to $\mathrm{dim}\, X$. In this note we show that some blow-ups of projective spaces satisfy Orlov's conjecture. This includes a blow-up of $\mathbb{P}^2$ in nine arbitrary distinct points, or a blow-up of three distinct points lying on an exceptional divisor of a blow-up of $\mathbb{P}^3$ in a line. In particular, our method gives an alternative proof of Orlov's con…
We prove that the redundant blow-up preserves the finite generation of the Cox ring of a rational surface under a suitable assumption, and we study the birational structure of Mori dream rational surfaces via redundant blow-ups. It turns out that the redundant blow-up completely characterizes birational morphisms of Mori dream rational surfaces with anticanonical Iitaka dimension $0$. As an application, we construct new Mori dream rational surfaces with anticanonical Iitaka dimension $0$ and $-\infty$ of arbitrarily large Picard number.
This text is an introduction to algebraic enumerative geometry and to applications of tropical geometry to classical geometry, based on a course given during the X-UPS mathematical days, 2008 May 14th and 15th. The aim of this text is to be understandable by a first year master student.
Linear systems on blow-ups of Hirzebruch surfaces
本文提出并证明了Hirzebruch曲面上关于线性系统的猜想，适用于特定点数的吹胀情况。
Negative curves on very general blow-ups of P^2
与Nagata猜想和Segre-Harbourne-Gimigliano-Hirschowitz猜想相关的一个猜想指出，在$¶^2$在非常一般的位置的点集上爆破时，任何具有负自相交的积分曲线都是（-1）-曲线。在本文中，我们验证了这一猜想的所有曲线，其图像上的$¶^2$是一个曲线的奇点的重数为2的中心之一的爆破。
The integral Chow ring of weighted blow-ups
该研究给出加权爆破的整 Chow 环计算公式，同时得到加权射影栈丛的整 Chow 环、加权爆破的 Gysin 同态公式与分裂原理的推广，并在附录中算出加权爆破的陈类。
We completely classify redundant blow-ups appearing in the theory of rational surfaces with big anticanonical divisor due to Sakai. In particular, we construct a rational surface with big anticanonical divisor which is not a minimal resolution of a del Pezzo surface with only rational singularities, which gives a negative answer to a question raised in a paper by Testa, Várilly-Alvarado, and Velasco.
Given an arbitrary projective birational morphism of varieties, we provide a natural and explicit way of constructing relative compactifications of the maps induced on the main components of the jet schemes. In the case the morphism is the Nash blow-up of a variety, such relative compactifications are shown to be given by the Nash blow-ups of the main components of the jet schemes.
Blow-ups of canonical singularities
本文应用Shokurov的归纳法研究了终端奇点和正则奇点。作为一个简单的后果的极小模型计划，我们表明，任何三维日志终端奇点存在一些特殊的，所谓的，plt爆破。我们讨论了它们的性质，并构造了一些例子。
We prove that certain Severi varieties of nodal curves of positive genus on general blow-ups of the twofold symmetric product of a general elliptic curve are non-empty and smooth of the expected dimension. This result, besides its intrinsic value, is an important preliminary step for the proof of nonemptiness of Severi varieties on general Enriques surfaces in arXiv:2109.10735.
We discuss automorphisms and pseudo-automorphisms on blowups of complex projective space with an eye to finding ones with interesting dynamical behavior.
Rationality of Seshadri constants on blow-ups of ruled surfaces
本文研究直纹曲面爆破上的 Seshadri 常数，提出分类负自交曲线的猜想，并在假设该猜想成立时构造出具有无理 Seshadri 常数的丰富线丛。
Blowing-ups describing the polarization change of moduli schemes of semistable sheaves of general rank
设$H$和$H'$是光滑射影曲面$X$上的两个样本线丛，而$M(H)$（分别为。$M(H')$）的粗模方案$H$ -半稳定的（分别为. $H'$ -半稳定）固定类型$(r,c_1,c_2)$的滑轮。我们构造了一个爆破序列，它描述了$M(H)$如何不同于$M(H')$，不仅当$r=2$，而且当$r$是任意的。我们在这里使用的手段是初等变换和带标志层的概念。
The paper has been withdrawn.
On the quantum cohomology of blow-ups of four-dimensional quadrics
本文研究四维二次曲面吹起的量子上同调，提出并验证与 Galkin 下界猜想相关的猜想，同时证明 Conjecture $\mathcal{O}$ 适用于两类吹起情形。
We consider weak Fano manifolds with small contractions obtained by blowing up successively curves and subvarieties of codimension 2 in products of projective spaces. We give a classification result for a special case. In the process of proof, we describe explicitly the structure of nef cones and compute the self intersection numbers of anti-canonical divisors for such weak Fano manifolds.
Torus actions, weighted blow-ups, and desingularization of plane curves
本文通过加权吹胀构造平面曲线的脱 singularization，利用环面作用和 equivariant 中心进行归纳论证，无需限制于完美基域。
Let $C \subset \mathbb{P}^2$ be an irreducible and reduced curve of degree $e > 0$. Let $X$ be the blow up of $\mathbb{P}^2$ at $r$ distinct smooth points $p_1,\ldots,p_r \in C$. We study line bundles on $X$ and establish conditions for ampleness and $k$-very ampleness.
Gromov-Witten invariants of blow-ups along submanifolds with convex normal bundles
给定X内的子流形Z，设Y是X沿Z的爆破。当Z在X中的法丛是凸的且有一个小的假设时，我们证明了Y的亏格为零的GW-不变量与X的GW-不变量是相同的。在同样的假设下，证明了一个消灭定理。这两个定理适用的一个例子是当法丛由整体瓣生成时。这两个主要定理不适用于任意爆破，并包括反例。
We prove that the sum of the $α$-invariants of two different Kollár components of a Kawamata log terminal singularity is less than $1$.
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。