Numerically trivial involutions of Kummer type of an Enriques surface

摘要

There are two types of numerically trivial involutions of an Enriques surface according to their period lattice. One is of U(2) ⊥ U(2)-type and the other is of (U(2) ⊥ U(2))-type. An Enriques surface with an involution of (U(2)⊥U(2))-type is doubly covered by a Kummer surface of product type, and such involutions are classified again into two types according to the parity of the corresponding Copel subgroups. Involutions of odd (U(2) ⊥ U(2))-type are constructed from the standard Cremona involutions of the quadric surface and closely related with quartic del Pezzo surfaces.