Fourier--Mukai partners of elliptic ruled surfaces
Hokuto Uehara
TL;DR
This paper investigates the relationships between elliptic ruled surfaces through Fourier--Mukai partners and describes their autoequivalence groups using derived category techniques.
Contribution
It provides a classification of Fourier--Mukai partners for elliptic ruled surfaces and characterizes their autoequivalence groups.
Findings
Classification of Fourier--Mukai partners for elliptic ruled surfaces.
Description of autoequivalence groups of derived categories.
Application of derived category methods to ruled surfaces with elliptic fibrations.
Abstract
We study Fourier--Mukai partners of elliptic ruled surfaces. We also describe the autoequivalence group of the derived categories of ruled surfaces with an elliptic fibration, by using \cite{Ue15}.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Algebraic structures and combinatorial models · Geometric and Algebraic Topology