Fourier-Mukai loci of K3 surfaces of Picard number one

TL;DR

This paper investigates the Fourier-Mukai locus of derived categories of K3 surfaces with Picard number one, revealing it is strictly smaller than the Matsui spectrum, thus advancing understanding of derived equivalences in algebraic geometry.

Contribution

The paper characterizes the Fourier-Mukai locus for K3 surfaces of Picard number one and compares it to the Matsui spectrum, providing new insights into derived categories.

Findings

Fourier-Mukai locus is explicitly described for these K3 surfaces.

The locus is strictly smaller than the Matsui spectrum.

Results deepen understanding of derived equivalences in algebraic geometry.

Abstract

In this paper, we describe the Fourier-Mukai locus of the derived category of a complex algebraic K3 surface of Picard number one. We also prove that the Fourier-Mukai locus of the derived category of a complex algebraic K3 surface of Picard number one is strictly smaller than it's Matsui spectrum.