Geometry and Physics Seminar: Xiaowei Wang

In order to construct the moduli space of canonical polarized manifolds, three different stability conditions have been introduced, namely, KSBA-stability, K-stabilty and asymptotic GIT stability. In this talk, we try to explore the relations among them. In particular, any canonical polarized manifold is stable with respect to all three conditions above, however the compactifications they give are different. As a consequence, we answer a longstanding question by showing that asymptotically GIT Chow semistable varieties do not form a proper family.