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Existence of weak Kähler-Einstein metrics on Q-Gorenstein smoothable Fano varieties and applications to the moduli problem

Cristiano Spotti
(University of Cambridge)
Onsdag, 13 april, 2016, at 14:15-15:15, in Aud. D3 (1531-215)
I will discuss how the Yau-Tian-Donaldson conjecture about the equivalence between existence of Kähler-Einstein metrics and K-polystability also holds for Q-Gorenstein smoothable Q-Fano varieties.
The main proof is based on the study of the Donaldson's cone angle continuity path in flat families. Moreover, I will show how this is related to the construction of an algebraic structure on the Gromov-Hausdorff compactification of the moduli space of KE Fano manifolds, with emphasis on the explicit case of del Pezzo surfaces. The talk is based on joint works with Y. Odaka, S. Sun and C. Yao.
Organiseret af: QGM
Kontaktperson: Jørgen Ellegaard Andersen