Algebraic deformations and Fourier--Mukai transforms for Calabi--Yau manifolds

TL;DR

This paper demonstrates that derived equivalences between Calabi--Yau manifolds extend to their deformations and provides a new proof of a specific derived equivalence involving Pfaffian and Grassmannian varieties.

Contribution

It establishes the extension of derived equivalences to general fibers of deformations for Calabi--Yau manifolds and offers a novel proof of the Pfaffian--Grassmannian equivalence.

Findings

Derived equivalences extend to deformations of Calabi--Yau manifolds.

New proof of Pfaffian--Grassmannian derived equivalence.

Enhanced understanding of deformation behavior in derived categories.

Abstract

Given a pair of derived-equivalent Calabi--Yau manifolds of dimension more than two, we prove that the derived equivalence can be extended to general fibers of versal deformations. As an application, we give a new proof of the Pfaffian--Grassmannian derived equivalence.