CMSA Geometry and Physics Seminar – The geometry of Maurer–Cartan equation near degenerate Calabi–Yau varieties


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June 22, 2020 9:30 am - 10:30 am
via Zoom Video Conferencing

Ziming Ma - CUHK

In this talk, we construct a dgBV algebra PV*(X) associated to a possibly degenerate Calabi--Yau variety X equipped with local thickening data. This gives a version of the Kodaira--Spencer dgLa which is applicable to degenerated spaces including both log smooth or maximally degenerated Calabi--Yau. We use this to prove an unobstructedness result about the smoothing of degenerated Log Calabi--Yau varieties X satisfying Hodge--deRham degeneracy property for cohomology of X, in the spirit of Kontsevich--Katzarkov--Pantev. This is a joint work with Kwokwai Chan and Naichung Conan Leung.