On some Fano--Enriques threefolds

2008/10/02 by Ilya Karzhemanov, Karzhemanov, Ilya
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.0810.0487

10 pages; minor changes, 4 references added, to appear in Advances in Geometry

arxiv created 2009/08/12 · arxiv updated 2009/12/01

Abstract

We give a classification of Fano threefolds X with canonical Gorenstein singularities such that X possess a regular involution, which acts freely on some smooth surface in |-K_X|, and the linear system |-K_X| gives a morphism which is not an embedding. From this classification one gets, in particular, a description of some natural class of Fano--Enriques threefolds.

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