Numerically trivial automorphisms of Enriques surfaces in characteristic 2

摘要

An automorphism of an algebraic surface S is called cohomo logically (numerically) trivial if it acts identically on the second cohomology group (this group modulo torsion subgroup). Extending the results of Mukai and Namikawa to arbitrary characteristic p > 0, we prove that the group of cohomologically trivial automorphisms Aut_(ct)(S) of an Enriques surface S is of order ≤ 2 if S is not supersingular. If p = 2 and S is supersingular, we show that Aut_(ct)(S) is a cyclic group of odd order n ∈ {1,2,3,5,7,11} or the quaternion group Qg of order 8 and we describe explicitly all the exceptional cases. If Ks ≠ 0, we also prove that the group Autnt(5) of numerically trivial automorphisms is a subgroup of a cyclic group of order ≤ 4 unless p = 2, where Aut_(nt)(S) is a subgroup of a 2-elementary group of rank ≤ 2.