Stability conditions on products of curves and Hilbert schemes of surfaces

TL;DR

This paper characterizes stability conditions on derived categories of product curves and constructs new stability conditions on Hilbert schemes of points on specific surfaces, advancing understanding in algebraic geometry.

Contribution

It uniquely determines stability conditions on product curves and develops stability conditions on Hilbert schemes of points on certain surfaces, including K3 surfaces of Kummer type.

Findings

Stability conditions on product curves are uniquely determined by central charge and skyscraper phase.

Constructed stability conditions on Hilbert schemes of points on specific surfaces.

Applied results to K3 surfaces of Kummer type.

Abstract

We prove that stability conditions on the derived category of a product of curves of positive genus are uniquely determined by their central charge and the phase of skyscraper sheaves. As an application, we construct stability conditions on Hilbert schemes of points on certain surfaces, including some K3 surfaces of Kummer type.