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Iskovskikh Seminar
April 12, 2012 18:00, Moscow, Steklov Mathematical Institute, room 540

"On standart models of conic fibrations" (A. Avilov), "Surfaces on Oeljeclaus–Toma manifolds" (S. Verbitskaya), "Canonical quotient singularities" (I. Krylov), "Terminal Fano threefolds with torsion in Weil divisors class group" (K. Khrabrov).

A. Avilov, S. Verbitskaya, I. Krylov, K. Khrabrov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

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Abstract: A. Avilov: In this talk I will prove an analog of Sarkisov's theorem about existence of a standard model for a 3-dimensional conic fibrations with group action and for a fibrations over a non-algebraically closed field.
S. Verbitskaya: Oeljeclaus–Toma Manifolds are complex non-Kähler manifolds. They were constructed by Karl Oeljeclaus and Matei Toma using number fields. These manifolds are generalizations of Inoue surfaces $S_m$. In this paper we show that there are no complex compact surfaces on Oeljeclaus–Toma manifolds except Inoue surfaces.
I. Krylov: There is a hypothesis which states, that index of isolated canonical singularities is not more than $f(n)$, where $n$ is dimension of the variety. We prove that this is right in case of dimension 3 and $f(3)=4$.
K. Khrabrov: In this work we classify $\mathbb{Q}-$Fano threefolds with Fano index greater than 1 and with nontrivial torsion in Weil divisors class group. Singularities of such threefolds can be found in a small list and all such threefolds can be realized as quotients of complete intersections in weighted projective spaces by the action of a finite group.

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