On two-elementary K3 surfaces with finite automorphism group

Abstract

We study complex algebraic K3 surfaces of Picard ranks 11,12, and 13 of finite automorphism group that admit a Jacobian elliptic fibration with a section of order two. We prove that the K3 surfaces admit a birational model isomorphic to a projective quartic hypersurface and construct geometrically the frames of all supported Jacobian elliptic fibrations. We determine the dual graphs of all smooth rational curves for these K3 surfaces, the polarizing divisors, and the embedding of the reducible fibers in each frame into the corresponding dual graph.

33 pages

References in corpus (7)

• Elliptic fibrations on K3 surfaces
• The duality between F-theory and the Heterotic String in $D=8$ with two Wilson lines
• Elliptic fibrations on covers of the elliptic modular surface of level 5
• On K3 surfaces of Picard rank 14
• Counting elliptic fibrations on K3 surfaces
• On the duality of F-theory and the CHL string in seven dimensions
• On Néron-Severi lattices of Jacobian elliptic K3 surfaces

Cited by in corpus (1)

• K3 Surfaces and Orthogonal Modular Forms