Counting Twisted Tame Fourier-Mukai Partners of an Ordinary K3 Surface

TL;DR

This paper proves finiteness of tame twisted Fourier-Mukai partners for certain K3 surfaces over positive characteristic fields and provides a counting formula for ordinary cases, linking partners to moduli spaces of twisted sheaves.

Contribution

It establishes finiteness results and a counting formula for tame twisted Fourier-Mukai partners of K3 surfaces in positive characteristic, connecting them to moduli spaces.

Findings

Finiteness of tame twisted Fourier-Mukai partners for K3 surfaces.

A counting formula for ordinary tame untwisted K3 surfaces.

Every such partner is a moduli space of twisted sheaves.

Abstract

In this article, we prove that a tame twisted K3 surface over an algebraically closed field of positive characteristic has only finitely many tame twisted Fourier-Mukai partners and we give a counting formula in case we have an ordinary tame untwisted K3 surface. We also show that every tame twisted Fourier Mukai partner of a K3 surface of finite height is a moduli space of twisted sheaves over it.