Corpus ID: 119618942

Intersection cohomology of moduli spaces of vector bundles over curves

  title={Intersection cohomology of moduli spaces of vector bundles over curves},
  author={Sergey Mozgovoy and Markus Reineke},
  journal={arXiv: Algebraic Geometry},
We compute the intersection cohomology of the moduli spaces $M(r,d)$ of semistable vector bundles of arbitrary rank $r$ and degree $d$ over a curve. To do this, we introduce new invariants, called Donaldson-Thomas invariants of a curve, which can be effectively computed by methods going back to Harder, Narasimhan, Desale and Ramanan. Our main result relates the Hodge-Euler polynomial of the intersection cohomology of $M(r,d)$ to the Donaldson-Thomas invariants. More generally, we introduce… Expand
  • Mirko Mauri
  • Mathematics
  • Journal of the Institute of Mathematics of Jussieu
  • 2021
For $G = \mathrm {GL}_2, \mathrm {SL}_2, \mathrm {PGL}_2$ we compute the intersection E-polynomials and the intersection Poincaré polynomials of the G-character variety of a compactExpand
Intersection cohomology of moduli spaces of sheaves on surfaces
We study intersection cohomology of moduli spaces of semistable vector bundles on a complex algebraic surface. Our main result relates intersection Poincaré polynomials of the moduli spaces toExpand
Equivariant motivic Hall algebras.
We introduce a generalization of Joyce's motivic Hall algebra by combining it with Green's parabolic induction product, as well as a non-archimedean variant of it. In the construction, we followExpand
Quiver representations in abelian categories
We introduce the notion of (twisted) quiver representations in abelian categories and study the category of such representations. We construct standard resolutions and coresolutions of quiverExpand
Cohomological $\chi$-independence for moduli of one-dimensional sheaves and moduli of Higgs bundles
We prove that the intersection cohomology (together with the perverse and the Hodge filtrations) for the moduli space of one-dimensional semistable sheaves supported in an ample curve class on aExpand


Donaldson-Thomas invariants vs. intersection cohomology for categories of homological dimension one
The present paper is an extension of a previous paper written in collaboration with Markus Reineke dealing with quiver representations. The aim of the paper is to generalize the theory and to provideExpand
Twisted genera of symmetric products
We give a new proof of formulae for the generating series of (Hodge) genera of symmetric products X(n) with coefficients, which hold for complex quasi-projective varieties X with any kind ofExpand
Poincaré polynomials of the variety of stable bundles
§1. In this note, we indicate a few improvements to [3]. Let X be an irreducible, non-singular projective algebraic curve defined over a finite field Fq with q elements, of characteristic p. LetExpand
On the Abel-Jacobi map for divisors of higher rank on a curve
The aim of this paper is to present an algebro-geometric approach to the study of the geometry of the moduli space of stable bundles on a smooth projective curve defined over an algebraically closedExpand
The hodge numbers of the moduli spaces of vector bundles over a Riemann surface
Inductive formulas for the Betti numbers of the moduli spaces of stable holomorphic vector bundles of coprime rank and degree over a fixed Riemann surface of genus at least two were obtained byExpand
On the Chow motive of some moduli spaces
We study the motive of moduli spaces of stable vector bundles over a smooth projective curve. We prove this motive lies in the category generated by the motive of the curve and we compute its classExpand
Donaldson–Thomas invariants versus intersection cohomology of quiver moduli
Abstract The main result of this paper is the statement that the Hodge theoretic Donaldson–Thomas invariant for a quiver with zero potential and a generic stability condition agrees with theExpand
Moduli spaces of stable pairs and non-abelian zeta functions of curves via wall-crossing
In this paper we study and relate the non-abelian zeta functions introduced by Weng and invariants of the moduli spaces of arbitrary rank stable pairs over curves. We prove a wall-crossing formulaExpand
Cohomology of Quotients in Symplectic and Algebraic Geometry. (MN-31), Volume 31
These notes describe a general procedure for calculating the Betti numbers of the projective quotient varieties that geometric invariant theory associates to reductive group actions on nonsingularExpand
Vector Bundles Over an Elliptic Curve
Introduction THE primary purpose of this paper is the study of algebraic vector bundles over an elliptic curve (defined over an algebraically closed field k). The interest of the elliptic curve liesExpand