On autoequivalences of some Calabi--Yau and hyperk\"ahler varieties

TL;DR

This paper introduces a method to generate new autoequivalences for certain Calabi-Yau and hyperk"ahler varieties by extending from smooth projective surfaces to their Hilbert schemes of points.

Contribution

It presents a novel approach to constructing autoequivalences for complex varieties using Hilbert schemes, expanding the understanding of derived categories in algebraic geometry.

Findings

New autoequivalences constructed for specific Calabi-Yau and hyperk"ahler varieties

Method applicable to varieties derived from smooth projective surfaces

Enhances the toolkit for studying derived categories of complex varieties

Abstract

We show how one can construct new autoequivalences of some Calabi-Yau and hyperk"ahler varieties by passing from a smooth projective surface to the associated Hilbert scheme of points.