

Iskovskikh Seminar
September 20, 2012 18:00, Moscow, Steklov Mathematical Institute, room 540






Logcanonical thresholds under torus quotients
Hendrik Suss^{} ^{} M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

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Abstract:
The logcanonical threshold of a Fano variety $X$ is an invariant with
applications in birational geometry as well as in Kahler geometry. It is
defined with respect to a finite subgroup $G$ of $Aut(X)$. After chosing a
maximal torus $T$ in the automorphismen group of our Fano variety $X$ we
would like to reduce the computation of the logcanonical threshold on X
to that of a logcanonical threshold on some torus quotient $X=X/T$. As it
turns out, this works well if the following conditions are fulfilled:
(i) $G$ is contained in the normalizer of the maximal torus,
(ii) the $G$action on the characters given by conjugation has the trivial
character as its unique fixed point.
In this situation the $T$variety is called symmetric. As an application
we provide a criterion for the existence of Kahler–Einstein metrics on
symmetric Fano $T$varieties of complexity one.

