Derived categories of Gushel-Mukai surfaces and Fano fourfolds of K3 type

TL;DR

This paper investigates the derived categories of Gushel-Mukai surfaces and Fano fourfolds of K3 type, revealing non-isomorphism despite derived equivalence, and explores semiorthogonal decompositions in these geometries.

Contribution

It establishes that very general dual Gushel-Mukai surfaces are not isomorphic despite being derived and L-equivalent, and analyzes semiorthogonal decompositions for Fano fourfolds of K3 type.

Findings

Dual Gushel-Mukai surfaces are not isomorphic despite derived equivalence.

Semiorthogonal decompositions for Fano fourfolds of K3 type are characterized.

Answers a question by Bernardara-Fatighenti-Manivel-Tanturri regarding these decompositions.

Abstract

We prove that very general, dual Gushel-Mukai surfaces are not isomorphic, though derived and L-equivalent. We use this result to study two semiorthogonal decompositions for a family of Fano fourfolds of K3 type, answering a question by Bernardara-Fatighenti-Manivel-Tanturri.