Explicit exceptional collections for Johnson-Kollar stacks

Franco Rota (University of Glasgow)

Wednesday 6th October 16:00-17:00 Maths 110

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 DelPezzo 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.

All this is joint work (still in progress) with Giulia Gugiatti (ICTP).

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