Thirteenth Algorithmic Number Theory Symposium ANTS-XIII
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Zeta functions of nondegenerate hypersurfaces in toric varieties via controlled reduction in p-adic cohomology
Edgar Costa, David Harvey and Kiran S. Kedlaya
Abstract: We give an interim report on some improvements and generalizations of the Abbott-Kedlaya-Roe method to compute the zeta function of a nondegenerate ample hypersurface in a projectively normal toric variety over Fp in linear time in p. These are illustrated with a number of examples including K3 surfaces, Calabi-Yau threefolds, and a cubic fourfold. The latter example is a non-special cubic fourfold appearing in the Ranestad-Voisin coplanar divisor on moduli space; this verifies that the coplanar divisor is not a Noether-Lefschetz divisor in the sense of Hassett.
© 2017-2018 Jennifer Paulhus (with thanks to Kiran S. Kedlaya, and by extension Pierrick Gaudry and Emmanuel Thomé)