

Iskovskikh Seminar
December 17, 2015 18:00, Moscow, Steklov Mathematical Institute, room 540






KLTsingularities of horospherical pairs (after B.Pasquier,
arXiv:1509.06502)
E. Yu. Smirnov^{} ^{} National Research University "Higher School of Economics" (HSE), Moscow

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Abstract:
Let $X$ be a variety with an action of a reductive algebraic group $G$.
Recall that $X$ is said to be horospherical if it is a fibration over a
partial flag variety whose fiber is a smooth toric variety.
It turns out that for an effective $B$invariant $\mathbb Q$Cartier divisor
$D$ on $X$, such that $D+K_X$ is also $\mathbb Q$Cartier, the pair $(X,D)$
is Kawamata logterminal iff $D=\sum a_i D_i$, with $D_i$ irreducible and
$a_i\in [0,1)$.
The strategy of the proof is as follows: the case of horospherical $X$ can
be reduced to the case of a flag variety. And if $X$ is a partial flag
variety $G/P$, the klt condition can be reinterpreted combinatorially in
terms of the root systems for $G$ and $P$, using Bott–Samelson
desingularizations.

