Talk page
Title:
Nonlinear optimal degeneration problem for Fano varieties
Speaker:
Abstract:
For any Q-Fano variety, we first introduce a nonlinear $\tilde{\beta}$-functional on the space of real valuations. We use the tools from birational algebraic geometry to show the existence of minimizers. We then prove that the minimizing valuation that induces a special R-test configuration is unique, and has a K-semistable Fano central fibre $(W, \xi)$. Moreoverthere is a unique K-polystable degeneration of $(W, \xi)$. As an application, we confirm the conjecture of Chen-Sun-Wang about the algebraic-uniqueness for normalized K\"{a}hler-Ricci flow limits on Fano manifolds. The results/techniques are global analogues of local counterparts in the study normalized volume functional of valuations (centered at a closed point). This is a joint work with Jiyuan Han.
Link:
Workshop: