Quotients of K3 Surfaces Modulo Involutions

1999/05/30 by D. -Q. Zhang, Zhang, D. -Q.
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Primary : 14J28 #Secondary : 14J27 #math.AG #msc:14J27 #msc:14J28

paper · pdf · doi:10.48550/arxiv.math/9905193

30 pages. Japanese J. Mathematics, to appear

arxiv created 1999/05/30 · arxiv updated 2009/11/30

Abstract

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).

Related

• K3 surfaces with two involutions and low Picard number
• On strictly elliptic K3 surfaces and del Pezzo surfaces
• Elliptic fibrations and involutions on K3 surfaces
• Enriques surfaces with normal K3-like coverings
• Involutions on surfaces with p_g=q=0 and K²=3