Derived categories of families of Fano threefolds

Published 24 Feb 2022 in math.AG | (2202.12345v2)

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 $X/S$.

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Alexander Kuznetsov

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