PIRSA:10050033

Normal Forms for Lattice Polarized K3 Surfaces and the Kuga-Satake Hodge Conjecture

Doran, C. (2010). Normal Forms for Lattice Polarized K3 Surfaces and the Kuga-Satake Hodge Conjecture. Perimeter Institute. https://pirsa.org/10050033

Doran, Charles. Normal Forms for Lattice Polarized K3 Surfaces and the Kuga-Satake Hodge Conjecture. Perimeter Institute, May. 07, 2010, https://pirsa.org/10050033 

          @misc{ pirsa_PIRSA:10050033,
            doi = {10.48660/10050033},
            url = {https://pirsa.org/10050033},
            author = {Doran, Charles},
            keywords = {Quantum Fields and Strings},
            language = {en},
            title = {Normal Forms for Lattice Polarized K3 Surfaces and the Kuga-Satake Hodge Conjecture},
            publisher = {Perimeter Institute},
            year = {2010},
            month = {may},
            note = {PIRSA:10050033 see, \url{https://pirsa.org}}
          }

Charles Doran

DOI 10.48660/10050033
Collection
Talk Type Conference
Subject

Abstract

We introduce a projective hypersurface ''normal form'' for a class of K3 surfaces which generalizes the classical Weierstrass normal form for complex elliptic curves. A geometric two-isogeny relates these K3 surfaces to the Kummer K3 surfaces of principally polarized abelian surfaces, with the normal form coefficients naturally identifying with the Igusa basis of Siegel modular forms of degree two. These results are reinterpreted through the lens of the Kuga-Satake Hodge Conjecture, and seen as a prediction coming from mirror symmetry.