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