Algebraic Geometry Seminar Wednesday March 10th, 2021
Time:	8:00 PM - 9:15 PM
Title:	**SPECIAL TIME** Non-variety but canonical "tropical" geometric compactification of moduli of hyperKahler manifolds, and PL functions associated to type II degenerations of K3 surfaces
Speaker:	Yuji Odaka, Kyoto University
Abstract:
This talk is based on joint work with Yoshiki Oshima (Osaka university). While natural (“KSBA type”) projective compactification of moduli \F_{2d} of algebraic K3 surfaces depends on choice of ample Q-divisors, hence there are non-unique, we discuss a certain non-variety but canonical explicit compactification by mainly using classical works of Siegel/Satake/Morgan-Shalen. It conjecturally parametrizes the limits of the canonical (hyperKahler) metrics and also captures “tropicalizations”, as expected in the context of SYZ mirror symmetry. Our approach also naturally extends to compact hyperKahler manifolds as we discuss. General framework and details study in 2-dim type III degeneration case is in our monograph arXiv:1810.07685. Its type II degeneration case is discussed in arXiv:2010.00416 which interestingly observes an unexpected relation with the work of Alexeev-Brunyate-Engel’20. Not only that aspect, it may be generally interesting to compare with Philip Engel’s next talk and their very nice joint papers.