Time: 10:00-11:30 March 18, 2025 (Tuesday)
Venue: MCM410
Title: K-moduli spaces of certain families of weighted projective hypersurfaces and the structure of wall-crossing
Abstract: In the talk, we will consider the K-moduli spaces of hypersurfaces of degree 2(n+3) in weighted projective spaces P(1,2,n+2,n+3). We give an explicit description of the wall crossing for K-moduli spaces M_w of certain log Fano pairs with coefficient w whose double cover gives the weighted hypersurface. By this description, we show that the K-polystable limits of these weighted hypersurfaces are also weighted hypersurfaces of the same degree in the same weighted projective space. Furthermore, we obtain that the wall crossing of M_w coincides with variation of GIT except at the last K-moduli wall which gives a divisorial contraction. Our K-moduli spaces provide new birational models for some natural loci in the moduli space of marked hyperelliptic curves. This is based on my work with In-Kyun Kim and Yuchen Liu.
