Normal functions, Picard-Fuchs equations, and elliptic fibrations on K3 surfaces

作者：Chen Xi^*; Doran Charles; Kerr Matt; Lewis James D

来源：Journal fur die Reine und Angewandte Mathematik, 2016, 721(721): 43-79.

DOI：10.1515/crelle-2014-0085

Using Gauss-Manin derivatives of generalized normal functions, we arrive at results on the non-triviality of the transcendental regulator for K-m of a very general projective algebraic manifold. Our strongest results are for the transcendental regulator for K-1 of a very general K3 surface and its self-product. We also construct an explicit family of K-1 cycles on H circle plus E-8 circle plus E-8-polarized K3 surfaces, and show they are indecomposable by a direct evaluation of the real regulator. Critical use is made of natural elliptic fibrations, hypersurface normal forms, and an explicit parametrization by modular functions.

• 出版日期2016-12