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

## TL;DR

This paper derives explicit generating functions for elliptic genera on Hilbert schemes of points and moduli spaces of sheaves on K3 surfaces, advancing the understanding of their geometric and topological properties.

## Contribution

It provides refined formulas for elliptic genera on these moduli spaces, extending previous results with new explicit computations.

## Key findings

- Generated formulas for elliptic genera on Hilbert schemes of points.
- Computed elliptic genera for moduli spaces of sheaves on K3 surfaces.
- Extended Verlinde formulas to new geometric contexts.

## 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.