

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


Abstract:
A. Avilov:
In this talk I will prove an analog of Sarkisov's theorem about existence of
a standard model for a 3dimensional conic fibrations
with group action and for a fibrations over a nonalgebraically closed
field.
S. Verbitskaya:
Oeljeclaus–Toma Manifolds are complex nonKähler 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.

