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Derived Categories of Families of Sextic del Pezzo Surfaces

International Mathematics Research Notices. 2021. Vol. 2021. No. 12. P. 9262–9339.
Kuznetsov A.

We construct a natural semiorthogonal decomposition for the derived category of an arbitrary flat family of sextic del Pezzo surfaces with at worst du Val singularities. This decomposition has three components equivalent to twisted derived categories of finite flat schemes of degrees 1, 3, and 2 over the base of the family. We provide a modular interpretation for these schemes and compute them explicitly in a number of standard families. For two such families the computation is based on a symmetric version of homological projective duality for P2 × P2 and P1 × P1 × P1, which we explain in an appendix.

Research target: Mathematics
Language: English
DOI
Text on another site
Keywords: derived categorysextic del Pezzo surface
Publication based on the results of:
Algebraic varieties from the point of view of derived categories, homological algebra, special holonomy metrics and classical algebraic geometry (2022)
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