Speaker: Sergey Galkin
Title: (Two constructions for) Mirrors of Fano varieties
Date: Dec 14, 2010, 17:30 - 17:45
Place: Universidade Federal do Parana, Curitiba
I will review two constructions of mirror-dual partners for Fano varieties (joint works with A. Bondal, T. Coates and A. Corti). Both constructions have their roots in a work of Eguchi, Hori and Xiong: one (Minkowski ansatz) is a recipe for cooking mirrors using toric degenerations, another exploits descent to a variety of lines to produce a mirror of a minuscule homogeneous variety. The Minkowski ansatz is general enough to provide an answer for all Fano surfaces and threefolds, but in its current state it is merely a phenomenology. Minuscule descent is very refined, but highlights some geometry that probably has to be used in general.