Perelman's entropy and optimal degeneration

Abstract: Algebraic optimal degeneration of Fano variety along Kahler-Ricci flow was originally constructed by Chen-Sun-Wang and was deepened by Dervan-Szekelyhidi, Han-Li and recent Blum-Liu-Xu-Zhuang. The degeneration is a substantial intermediate for studying a Fano variety with Kahler-Ricci soliton appearing in the Gromov-Hausdorff limit of Kahler-Ricci flow. The degeneration is characterized by a valuation which maximizes `H-entropy' among all valuations. Motivated by these works, I would like to explain my ongoing attempt to optimal degeneration of polarized variety with respect to `mu-entropy'. The mu-entropy appears in my study on mu-cscK metrics and muK-stability, which I introduced to understand cscK metrics and Kahler-Ricci soliton in a unified way. Going deep into the story, we encounter Perelman's entropy, which turns out to be the origin of our story.

algebraic geometry

Audience: researchers in the topic

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