

Iskovskikh Seminar
January 29, 2015 17:00, Moscow, Steklov Mathematical Institute, room 540






Quotients of cubic surfaces
A. S. Trepalin^{} ^{} A. A. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow

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Abstract:
We consider the following problem: whether the quotient of cubic surface
over algebraically nonclosed field by a finite group of automorphisms is
rational. We show, that the quotient can be nonrational only if the group
is trivial or a cyclic group of order 3 acting on the cubic surface in
definite way. Moreover, for this action we construct an explicit criterion
of rationality of the quotient in terms of Galois group.

