Automorphisms of unnodal Enriques surfaces

Abstract

It follows from an observation of A. Coble in 1919 that the automorphism group of an unnodal Enriques surface contains the $2$-congruence subgroup of the Weyl group of the $E_{10}$-lattice. In this article, we determine how much bigger the automorphism group of an unnodal Enriques surface can be. Furthermore, we show that the automorphism group is in fact equal to the $2$-congruence subgroup for generic Enriques surfaces in arbitrary characteristic (under the additional assumption that the Enriques surface is ordinary if the characteristic is $2$), improving the corresponding result of W. Barth and C. Peters for very general Enriques surfaces over the complex numbers.

arXiv comment22 pages, comments welcome

References in corpus (6)

• Elliptic Surfaces
• Moduli and periods of simply connected Enriques surfaces
• Numerically trivial automorphisms of Enriques surfaces in characteristic $2$
• Lagrangian tens of planes, Enriques surfaces and holomorphic symplectic fourfolds
• Congruence subgroups and Enriques surface automorphisms
• Bi-canonical representations of finite automorphisms acting on Enriques surfaces

Cited by in corpus (1)

• Infinitesimal automorphisms of algebraic varieties and vector fields on elliptic surfaces