

Iskovskikh Seminar
March 12, 2015 18:00, Moscow, Steklov Mathematical Institute, room 540






Fano–Enriques threefolds of big genus; the case of conic bundle
E. Gorinov^{} ^{} Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

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Abstract:
A pair $(U,A)$ is called a Fano–Enriques threefold if $U$ is a projective
normal threefold and $A$ is an ample
effective Cartier divisor on $U$ and $A$ is a smooth Enriques surface. A
natural discrete of a pair is an integer number $g = A^3/2 + 1$ called genus
of $(U,A)$.
Prokhorov suggested a method to classify such threefolds. In particular he
proved a sharp bound $g \leqslant 17$.
We show that that there is better bound: either $g = 17$ or $g \leqslant
13$.
Logminimal model program reduces studying of $U$ to studying a Mori fiber
space.
We discuss the most interesting case of conic bundle.

