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Refined Verlinde formulas for Hilbert schemes of points and moduli spaces of sheaves on K3 surfaces

Lothar Göttsche

Abstract

We compute generating functions for elliptic genera with values in line bundles on Hilbert schemes of points on surfaces. As an application we also compute generating functions for elliptic genera with values in determinant line bundles on moduli spaces of sheaves on K3 surfaces.

Refined Verlinde formulas for Hilbert schemes of points and moduli spaces of sheaves on K3 surfaces

Abstract

We compute generating functions for elliptic genera with values in line bundles on Hilbert schemes of points on surfaces. As an application we also compute generating functions for elliptic genera with values in determinant line bundles on moduli spaces of sheaves on K3 surfaces.

Paper Structure

This paper contains 8 sections, 11 theorems, 56 equations.

Table of Contents

  1. Introduction
  2. Background material
  3. Hilbert schemes of points
  4. Elliptic genus.
  5. Beauville-Bogomolov quadratic form
  6. The case $r=0$.
  7. The case of Hilbert schemes of points on K3 surfaces
  8. Moduli of sheaves on K3 surfaces

Key Result

Theorem \oldthetheorem

Let $S$ be an algebraic surface, $L\in \operatorname{Pic}(S)$. Then

Theorems & Definitions (16)

  • Theorem \oldthetheorem
  • Corollary \oldthetheorem
  • Theorem \oldthetheorem
  • Corollary \oldthetheorem
  • Theorem \oldthetheorem
  • Theorem \oldthetheorem
  • Corollary \oldthetheorem
  • Proposition \oldthetheorem
  • proof
  • Corollary \oldthetheorem
  • ...and 6 more