On the volumes of log canonical surfaces
Date/Time:18 Jul 2019 14:00
Venue: S17 #04-04 SR3
Speaker: Liu Wenfei, Xiamen University
On the volumes of log canonical surfaces
The geography of singular surfaces acquires more complexity due to their volumes, which are only rational numbers rather than integers. By a fundamental result of Alexeev, the set of volumes of all projective log canonical surfaces satisfies the so-called descending chain condition (DCC), if the coefficients of the boundary divisors belong to a given DCC set.
In this talk I will report on some recent progress on accumulation points and the minima of the volume sets for different classes of log canonical surfaces. As an application, one obtains a Noether type inequality for nonnormal stable surfaces. The talk is mostly based on joint work with Valery Alexeev.
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