Derived categories of families of Fano threefolds

We construct S-linear semiorthogonal decompositions of derived categories of smooth Fano threefold fibrations X/S with relative Picard rank 1 and rational geometric fibers and discuss how the structure of components of these decompositions is related to rationality properties of X/S.

Authors

Publication Details

Journal
Algebraic geometry
Published
2025-06-18
DOI
https://doi.org/10.14231/ag-2025-015
Primary Topic
Algebraic Geometry and Number Theory
Type
article
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article

Derived categories of families of Fano threefolds

Alexander Kuznetsov
Algebraic geometry
Algebraic Geometry and Number Theory
article

Derived categories of families of Fano threefolds

Alexander Kuznetsov
article en

Abstract

We construct S-linear semiorthogonal decompositions of derived categories of smooth Fano threefold fibrations X/S with relative Picard rank 1 and rational geometric fibers and discuss how the structure of components of these decompositions is related to rationality properties of X/S.

Algebraic geometry
Openalex Percentile: Top 81%
Algebraic Geometry and Number Theory
DOIOpen Access PDFOpenAlex
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Derived categories of families of Fano threefolds — Alexander Kuznetsov · Algebraic geometry (2025) | TGRS Research Map | TGRS