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Elliptic fibrations on K3 surfaces with large Picard rank

Banff International Research Station for Mathematical Innovation and Discovery

In this talk, we give an explicit description for the relation between algebraic Kummer surfaces of Jacobians of genus-two curves with principal polarization and those associated to (1, 2)-polarized abelian surfaces from three different angles: the point of view of 1) the binational geometry of quartic surfaces in P^3 using even-eights, 2) elliptic fibrations on K3 surfaces of Picard-rank 17 over P^1 using Nikulin involutions, 3) theta-functions of genus-two using two-isogeny. Finally, we will explain how these (1,2)-polarized Kummer surfaces naturally allow for an identification of the complex gauge coupling in Seiberg-Witten gauge theory with the axion-dilaton modulus in string theory using an old idea of Sen. (This is joint work with Adrian Clingher.)

Mathematics; Algebraic geometry; Relativity and gravitational theory; Mathematical physics

video/mp4

Author affiliation: Utah State University

2018-07-24

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/66566

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/