Computing Cup-Products in integral cohomology of Hilbert schemes of points on K3 surfaces

TL;DR

This paper investigates the structure of cup products in the integral cohomology of Hilbert schemes of points on K3 surfaces and provides a computational tool to analyze these products.

Contribution

It introduces a computer program to compute cup products in the cohomology of Hilbert schemes of K3 surfaces and addresses the representation of classes as products of lower degrees.

Findings

Developed a computational method for cup products

Identified classes representable as products of lower degrees

Enhanced understanding of cohomology ring structure

Abstract

We study cup products in integral cohomology of the Hilbert scheme of $n$ points on a K3 surface and present a computer program for this purpose. In particular, we deal with the question, which classes can be represented by products of lower degrees.