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Quotients of Fano surfaces. (English) Zbl 1252.14023
The paper under review deals with Fano surfaces \(S\) with a non-trivial automorphism group and their quotients.
The main tools used in this study are the computation of invariants on quotients, intersection theory on normal surfaces and the properties of the smooth cubic threefold whose lines are parametrized by \(S\).
All the possible cases are examined: cyclic groups of order 2,3,4,5,11,15 and non-cyclic groups \((\mathbb Z/2\mathbb Z)^2\), \(\mathbb D_2\), \((\mathbb Z/3\mathbb Z)^2\), \(\mathcal S_3\), \(\mathbb D_3\), \(\mathbb D_5\) and \(G\) (a group generated by two involution of type I whose product has order 3 and a type III(1) automorphism). For each group the quotient singularities and the main invariants are explicitly determined.
MSC:
14J29 Surfaces of general type
14J17 Singularities of surfaces or higher-dimensional varieties
14J50 Automorphisms of surfaces and higher-dimensional varieties
14C17 Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry
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