Generalized Kähler-Ricci flow on toric Fano varieties

Apostolov, Vestislav; Streets, Jeffrey; Ustinovskiy, Yury

doi:10.1090/tran/8619

Generalized Kähler-Ricci flow on toric Fano varieties
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by Vestislav Apostolov, Jeffrey Streets and Yury Ustinovskiy PDF

Trans. Amer. Math. Soc. 375 (2022), 4369-4409 Request permission

Abstract:

We study the generalized Kähler-Ricci flow with initial data of symplectic type, and show that this condition is preserved. In the case of a Fano background with toric symmetry, we establish global existence of the normalized flow. We derive an extension of Perelman’s entropy functional to this setting, which yields convergence of nonsingular solutions at infinity. Furthermore, we derive an extension of Mabuchi’s $K$-energy to this setting, which yields weak convergence of the flow.

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