
TL;DR
This paper studies the category of coherent sheaves on the generic fiber of flat proper families of algebraic varieties, establishing new results on derived equivalences and Fourier--Mukai partners through deformation techniques.
Contribution
It introduces a description of the coherent sheaves on the generic fiber as a Serre quotient and applies this to prove specialization of derived equivalences and find new Fourier--Mukai partners.
Findings
Describes the category of coherent sheaves on the generic fiber as a Serre quotient.
Proves the specialization of derived equivalence in families.
Provides new examples of Fourier--Mukai partners via deformation.
Abstract
For flat proper families of algebraic varieties with a smooth fiber, we describe the abelian category of coherent sheaves on the generic fiber as a Serre quotient. As an application, we prove specialization of derived equivalence. As another application, we provide new examples of Fourier--Mukai partners via deformations.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Algebraic structures and combinatorial models · Nonlinear Waves and Solitons
