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Home » BGMS Seminar: Openness of uniform K-stability in families of Q-Fano varieties

Seminar

BGMS Seminar: Openness of uniform K-stability in families of Q-Fano varieties February 28, 2019 (01:30 PM PST - 02:30 PM PST)
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Location: MSRI: Simons Auditorium
Speaker(s) Yuchen Liu (Yale University)
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K-stability is the algebraic notion which is supposed to characterize whether a Fano variety admits a K\"ahler-Einstein metric. One important feature of the notion of K-stability is that it is supposed to give a nicely behaved moduli space. To construct the K-moduli space of Q-Fano varieties as an algebraic space, one important step is to prove the openness of K-(semi)stable locus in families. In this talk, I will explain the proof of openness of uniform K-stability in families of Q-Fano varieties. This is achieved via showing the lower semi-continuity of delta-invariant, an interesting invariant introduced by Fujita and Odaka as a variant of Tian's alpha-invariant. This is a joint work with Harold Blum.

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