Indecomposable parabolic bundles and the existence of matrices in prescribed conjugacy class closures with product equal to the identity

On matrices in prescribed conjugacy classes with no common invariant subspace and sum zero

We determine those k-tuples of conjugacy classes of matrices, from which it is possible to choose matrices which have no common invariant subspace and have sum zero. This is an additive version of the Deligne-Simpson problem. We deduce the result from earlier work of ours on preprojective algebras and the moment map for representations of quivers. Our answer depends on the root system for a Kac-Moody Lie algebra.

Higgs bundles and indecomposable parabolic bundles over the projective line

In this paper we count the number of isomorphism classes of geometrically indecomposable quasi-parabolic structures of a given type on a given vector bundle on the projective line over a finite field. We give a conjectural cohomological interpretation for this counting using the moduli space of Higgs fields on the given vector bundle over the complex projective line with prescribed residues. We prove a certain number of results which bring evidences to the main conjecture. We detail the case of rank 2 vector bundles.

Parabolic bundles, products of conjugacy classes, and quantum cohomology

In this version referee's comments have been incorporated. Besides minor corrections, new material has been added on irrational markings. To appear in Ann. Inst. Fourier. We prove a condition for the existence of flat bundles on the punctured two-sphere with prescribed holonomies around the punctures, involving Gromov-Witten invariants of generalized flag varieties. This generalizes the case of special unitary bundles described by S. Agnihotri and the second author and independently P. Belkale.

在伴随轨道中具有规定条目的矩阵枚举

Enumerating matrices with prescribed entries in an adjoint orbit

研究有限域上方阵共轭类与仿射坐标子空间的交集，给出部分定义线性映射扩展为具有给定相似不变量的自同态数的Hall标量积公式，并应用于计数具有给定Smith标准形和行列式的矩阵多项式。

ACM vector bundles on prime Fano threefolds and complete intersection Calabi Yau threefolds

In this paper we derive a list of all the possible indecomposable normalized rank--two vector bundles without intermediate cohomology on the prime Fano threefolds and on the complete intersection Calabi Yau threefolds, say $V$, of Picard number $ρ=1$. For any such bundle $\E$, if it exists, we find the projective invariants of the curves $C \subset V$ which are the zero-locus of general global sections of $\E$. In turn, a curve $C \subset V$ with such invariants is a section of a bundle $\E$ from our lists. This way we reduce the problem for existence of such bundles on $V$ to the problem for …