Quotients of K3 Surfaces Modulo Involutions

Details Quotients of K3 Surfaces Modulo Involutions Quotients of K3 Surfaces Modulo Involutions

1999-05-30

arxiv.org/abs/math/9905193v1

Mathematics

Algebraic Geometry

30 pages. Japanese J. Mathematics, to appear

Scientific paper

Let X be a K3 surface with an involution g which has non-empty fixed locus X^g and acts non-trivially on a non-zero holomorphic 2-form. We shall construct all such pairs (X, g) in a canonical way, from some better known double coverings of log del Pezzo surfaces of index at most 2 or rational elliptic surfaces, and construct the only family of each of the three extremal cases where X^g contains 10 (maximum possible) curves. We also classify rational log Enriques surfaces of index 2. Our approach is more geometrical rather than lattice-theoretical (see Nikulin's paper for the latter approach).

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