Nikulin involutions and the CHL string

TL;DR

This paper explores special curve configurations on Jacobian elliptic K3 surfaces and their relation to string dualities, revealing new geometric structures and their implications in string theory.

Contribution

It introduces a detailed analysis of even-eight curve configurations on K3 surfaces and connects these geometric structures to the CHL string dualities.

Findings

Identification of specific curve configurations on K3 surfaces

Connection between geometric structures and string dualities

Discussion of non-generic K3 surface cases

Abstract

We study certain even-eight curve configurations on a specific class of Jacobian elliptic K3 surfaces with lattice polarizations of rank ten. These configurations are associated with K3 double covers, some of which are elliptic but not Jacobian elliptic. Several non-generic cases corresponding to K3 surfaces of higher Picard rank are also discussed. Finally, the results and the construction in question are interpreted in the context of the string dualities linked with the eight-dimensional CHL string.