Algebraic K-theory of toric hypersurfaces

By M. Kerr, Charles F. Doran. 2008

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We construct classes in the motivic cohomology of certain 1-parameter families of Calabi-Yau hypersurfaces in toric Fano n-folds, with applications to local mirror symmetry (growth of genus 0 instanton numbers) and inhomogeneous Picard-Fuchs equations. In the case where the family is classically modular the classes are related to Belinson's Eisenstein symbol; the Abel-Jacobi map (or rational regulator) is computed in this paper for both kinds of cycles. For the "modular toric" families where the cycles essentially coincide, we obtain a motivic (and computationally effective) explanation of a phenomenon observed by Villegas, Stienstra, and Bertin.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/a119736acbccf61d7fd2392363b29337f5e68be9

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In Discrete Mathematics and Combinatorics

In Geometry and Topology

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The elliptic dilogarithm for the sunset graph (2013, background): “For more on this sort of calculation, one can see [33].”