Derived equivalent conjugate K3 surfaces

TL;DR

This paper demonstrates that there are complex projective K3 surfaces and automorphisms of the complex numbers such that their conjugates are non-isomorphic Fourier-Mukai partners, revealing new relationships in derived categories of K3 surfaces.

Contribution

It establishes the existence of conjugate K3 surfaces that are non-isomorphic but share derived equivalence, expanding understanding of automorphisms and derived categories.

Findings

Existence of conjugate K3 surfaces that are Fourier-Mukai partners

Construction of automorphisms of complex numbers linking non-isomorphic K3 surfaces

New insights into the relationship between conjugation and derived equivalence

Abstract

We show that there exist a complex projective K3 surface $X$ and an automorphism of the complex numbers $\sigma$ such that the conjugate K3 surface $X^\sigma$ is a non-isomorphic Fourier-Mukai partner of $X$.