I. Coanda, A. Tikhomirov, G. Trautmann
We prove that the space of mathematical instantons with second Chern class 5 over ${\mathbb P}_3$ is smooth and irreducible. Unified and simple proofs for the same statements in case of second Chern class $\leq 4$ are contained.
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
Rationality of instanton moduli
本文在Tikhomirov关于奇数荷瞬子模空间不可约性结果的基础上，证明了瞬子模空间的合理性，从而得到所有奇数荷及荷2、4的瞬子模空间均为有理的。
The problem of irreducibility of the moduli space I_n of rank-2 mathematical instanton vector bundles with arbitrary positive second Chern class n on the projective 3-space is considered. The irreducibility of I_n was known for small values of n: Barth 1977 (n=1), Hartshorne 1978 (n=2), Ellingsrud and Stromme 1981 (n=3), Barth 1981 (n=4), Coanda, Tikhomirov and Trautmann 2003 (n=5). In this paper we prove the irreducibility of I_n for an arbitrary odd n.
In order to obtain existence criteria for orthogonal instanton bundles on $\mathbb{P}^n$, we provide a bijection between equivalence classes of orthogonal instanton bundles with no global sections and symmetric forms. Using such correspondence we are able to provide explicit examples of orthogonal instanton bundles with no global sections on $\mathbb{P}^n$ and prove that every orthogonal instanton bundle with no global sections on $\mathbb{P}^n$ and charge $c\geq 3$ has rank $r\leq (n-1)c$. We also prove that when the rank $r$ of the bundles reaches the upper bound, $\mathcal{M}_{\mathbb{P}^n}…
We prove the rationality and irreducibility of the moduli space of---what we call---the endomorphism-general instanton vector bundles of arbitrary rank on the projective space. In particular, we deduce the rationality of the moduli spaces of rank-two mathematical instantons. This problem was first studied by Hartshorne, Hirschowitz-Narasimhan in the late 1970s, and it has been reiterated within the framework of the ICM 2018.
We study the scheme of multi-jumping lines of an $n$-instanton bundle mainly for $n\leq 5$. We apply it to prove the irreducibility and smoothness of the moduli space of 5-instanton. Some particular situations with higher $c_2$ are also studied.
Irreducibility, Smoothness, and Connectivity of Realization Spaces of Matroids and Hyperplane Arrangements
本文研究拟阵与超平面排列的实现空间，提出朴素维数并引入归纳连通拟阵，证明其实现空间光滑、不可约且为已知维数复空间的 Zariski 开集，进而推导排列模空间连通性与拟阵刚性。
Rationality and categorical properties of the moduli of instanton bundles on the projective 3-space
本文证明了射影3空间上任意秩和荷的数学瞬子丛模空间的有理性与不可约性，并揭示其构成幺半范畴，基于Barth-Hulek monad构造与Hirzebruch曲面稳定丛模空间分析。
Mathematical instanton bundles of rank 4 and $c_2=2$ on ${\mathbb P}^4$ have a smoothquasiprojective moduli space, which is shown via a direct GIT construction. A complete classification of jumping lines of these vector bundles is obtained. The duals of these bundles are described. Dimension computations and irreducibility proofs for some "interesting" subsets of the moduli space are presented. Restrictions of vector bundles from ${\mathbb P}^4$ to ${\mathbb P}^3$ are shown to produce mathematical instanton bundles on ${\mathbb P}^3$.
Let $V$ be a vector bundle over a smooth curve $C$. In this paper, we study twisted Brill--Noether loci parametrising stable bundles $E$ of rank $n$ and degree $e$ with the property that $h^0 (C, V \otimes E) \ge k$. We prove that, under conditions similar to those of Teixidor i Bigas and of Mercat, the Brill-Noether loci are nonempty, and in many cases have a component which is generically smooth and of the expected dimension. Along the way, we prove the irreducibility of certain components of both twisted and "nontwisted" Brill--Noether loci. We describe the tangent cones to the twisted Bril…
Let P^2_r be the projective plane blown up at r generic points. Denote by E_0,E_1,...,E_r the strict transform of a generic straight line on P^2 and the exceptional divisors of the blown-up points on P^2_r respectively. We consider the variety V of all irreducible curves C in |dE_0-d_1E_1-...-d_rE_r| with k nodes as the only singularities and give asymptotically nearly optimal sufficient conditions for its smoothness, irreducibility and non-emptyness. Moreover, we extend our conditions for the smoothness and the irreducibility on families of reducible curves. For r<10 we give the complete answ…
We analyse the Gorenstein locus of the Hilbert scheme of $d$ points on $\mathbb{P}^n$ i.e. the open subscheme parameterising zero-dimensional Gorenstein subschemes of $\mathbb{P}^n$ of degree $d$. We give new sufficient criteria for smoothability and smoothness of points of the Gorenstein locus. In particular we prove that this locus is irreducible when $d\leq 13$ and find its components when $d = 14$. The proof is relatively self-contained and it does not rely on a computer algebra system. As a by--product, we give equations of the fourth secant variety to the $d$-th Veronese reembedding of $…
We use a complex version of the celebrated Atiyah-Hitchin-Drinfeld-Manin matrix equations to construct admissible torsion-free sheaves on $\p^3$ and complex quantum instantons over our quantum Minkowski space-time. We identify the moduli spaces of various subclasses of sheaves on $\p^3$, and prove their smoothness. We also define the Laplace equation in the quantum Minkowski space-time, study its solutions and relate them to the admissibility condition for sheaves on $\p^3$.
We present a new family of monads whose cohomology is a stable rank two vector bundle on $\PP$. We also study the irreducibility and smoothness together with a geometrical description of some of these families. Such facts are used to prove that the moduli space of stable rank two vector bundles of zero first Chern class and second Chern class equal to 5 has exactly three irreducible components.
We present a new family of monads whose cohomology is a stable rank two vector bundle on $\mathbb{P}^3$. We also study the irreducibility and smoothness together with a geometrical description of some of these families. These facts are used to construct a new infinite series of rational moduli components of stable rank two vector bundles with trivial determinant and growing second Chern class. We also prove that the moduli space of stable rank two vector bundles with trivial determinant and second Chern class equal to 5 has exactly three irreducible rational components.
In this paper we describe the structure of the space of parabolic reductions, and their compactifications, of principal $G$-bundles over a smooth projective curve over an algebraically closed field of arbitrary characteristic. We first prove estimates for the dimensions of moduli spaces of stable maps to the twisted flag varieties $E/P$ and Hilbert schemes of closed subschemes of $E/P$ with same Hilbert polynomials as that of a $P$-reductions of $E$. This generalizes the earlier results of Mihnea Popa and Mike Roth to connected reductive groups and the results of Y. I. Holla and M. S. Narasimh…
Let $K$ be the compact Lie group $USp(N/2)$ or $SO(N, R)$. Let $M^K_n$ be the moduli space of framed K-instantons over $S^4$ with the instanton number $n$. By Donaldson (1984), $M^K_n$ is endowed with a natural scheme structure. It is a Zariski open subset of a GIT quotient of $μ^{-1}(0)$, where $μ$ is a holomorphic moment map such that $μ^{-1}(0)$ consists of the ADHM data. The purpose of the paper is to study the geometric properties of $μ^{-1}(0)$ and its GIT quotient, such as complete intersection, irreducibility, reducedness and normality. If $K=USp(N/2)$ then $μ$ is flat and $μ^{-1}(0)$ …
A holomorphic triple over a compact Riemann surface consists of two holomorphic vector bundles and a holomorphic map between them. After fixing the topological types of the bundles and a real parameter, there exist moduli spaces of stable holomorphic triples. In this paper we study non-emptiness, irreducibility, smoothness, and birational descriptions of these moduli spaces for a certain range of the parameter. Our results have important applications to the study of the moduli space of representations of the fundamental group of the surface into unitary Lie groups of indefinite signature, whic…
We prove generic regularity and Uhlenbeck-type compactification theorems for the moduli spaces of PU(2)-monopoles. Generic regularity is NOT obtained in the usual way (by applying Sard theorem to a smooth parameterized moduli space), since the parameterized moduli space can be a priori singular. We explain why, using the standard order 0-perturbations, one cannot get the smoothness of the parameterized moduli space. (The same difficulty arises in the case of ASD-Spin^c moduli spaces, so the definition of the Spin^c-polynomial invariants should be revised.) We show that the singular locus of th…
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。