Full exceptional collection for anticanonical log del Pezzo surfaces

Abstract: The homological mirror symmetry conjecture predicts a correspondence between the derived category of coherent sheaves of a variety and the symplectic data (packaged in the Fukaya category) of its mirror object. Motivated by this, we construct exceptional collections for (the smooth stacks associated with) a family of log del Pezzo surfaces known as the Johnson-Kollar series. These surfaces have quotient, non-Gorenstein, singularities. Thus, our computation will include on the one hand an application of the special McKay correspondence, and on the other the study of their minimal resolutions, which are birational to a degree 2 del Pezzo surface. This is all joint work with Giulia Gugiatti.

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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