RATIONAL SURFACES WITH A LARGE GROUP OF AUTOMORPHISMS

摘要

Let K be an algebraically closed field, and X be a projective surface defined over IK. The group of automorphisms Aut(X) acts on the Neron-Severi group of X This action preserves the intersection form and the canonical class K_x, and therefore provides a morphism from Aut(X) to the group of integral isometries O(K_x) of the orthogonal complement Kx . When X is rational, the image satisfies further constraints: It is contained in an explicit Coxeter subgroup W_x of O(K_x), and Wx has infinite index in O(K_x) as soon as the rank ρ(X) of the Neron-Severi group of X exceeds 11.