Gromov-Hausdorff limits of Kähler manifolds and algebraic geometry

Thời gian: 16:30 - 18:00, thứ năm, ngày 24/8/2023

Hình thức: Offline tại phòng 612 A6 và online qua google meet, cụ thể https://meet.google.com/yep-kbzk-eao?pli=1&authuser=1

Tóm tắt: Given a Calabi-Yau manifold with maximal volume growth, the asymptotic cone in the Gromov-Hausdorff sense is a normal affine variety by Donaldson-Sun, and can be constructed by algebraic methods. I will try to explain their theory, and its application to the classification of Calabi-Yau metrics on symmetric spaces.

It is likely that there is a one-to-one correspondence between K-stable valuations inside the Weyl chamber of the symmetric space, and Calabi-Yau metrics on the space with the asymptotic cone determined by the valuation. This is a sort of Yau-Tian-Donaldson correspondence for non-compact spaces. Work in progress