Six line configurations and string dualities

DOI10.1007/S00220-019-03372-0zbMATH Open1440.14179arXiv1806.07460OpenAlexW2809014199MaRDI QIDQ2326894

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Publication date: 10 October 2019

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Abstract: We study the family of K3 surfaces of Picard rank sixteen associated with the double cover of the projective plane branched along the union of six lines, and the family of its Van Geemen-Sarti partners, i.e., K3 surfaces with special Nikulin involutions, such that quotienting by the involution and blowing up recovers the former. We prove that the family of Van Geemen-Sarti partners is a four-parameter family of K3 surfaces with $Hoplus{E}_7(-1)oplus{E}_7(-1)$ lattice polarization. We describe explicit Weierstrass models on both families using even modular forms on the bounded symmetric domain of type $IV$. We also show that our construction provides a geometric interpretation, called geometric two-isogeny, for the F-theory/heterotic string duality in eight dimensions. As a result, we obtain novel F-theory models, dual to non-geometric heterotic string compactifications in eight dimensions with two non-vanishing Wilson line parameters.

Full work available at URL: https://arxiv.org/abs/1806.07460

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