Residual categories of quadric surface bundles

Abstract: The residual category (or the Kuznetsov component) of a quadric surface bundle is the non-trivial component in the derived category. It is equivalent to the twisted derived category of a double cover over the base when the quadric surface bundle has simple degeneration (fibers have corank at most 1). I will consider quadric surface bundles with fibers of corank at most 2 and describe their residual categories as (twisted) derived categories of some scheme in two situations: (1) when the bundle has a smooth section; (2) when the total space is smooth and the base is a smooth surface. The results can be applied to describe the residual categories of a (partial) resolution of nodal quintic del Pezzo threefolds, cubic fourfolds containing a plane and certain complete intersections of quadrics.

algebraic geometrycombinatorics

Audience: researchers in the topic

Online Nottingham algebraic geometry seminar

Series comments: Online geometry seminar, typically held on Thursday. This seminar takes place online via Microsoft Teams on the Nottingham University "Algebraic Geometry" team.

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