Monomial deformations of certain hypersurfaces and two hypergeometric functions

DOI10.1142/S1793042115501122zbMath1332.14028arXiv1411.5116MaRDI QIDQ3458268

Kazuaki Miyatani

Publication date: 18 December 2015

Published in: International Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1411.5116

zbMATH Keywords

hypergeometric functionsDwork familyunit-root

Mathematics Subject Classification ID

Finite ground fields in algebraic geometry (14G15) Generalized hypergeometric series, ({}_pF_q) (33C20) Formal groups, (p)-divisible groups (14L05)

Related Items (6)

A complete hypergeometric point count formula for Dwork hypersurfaces ⋮ Zeta functions of alternate mirror Calabi-Yau families ⋮ Counting points with Berglund–Hübsch–Krawitz mirror symmetry ⋮ Hypergeometric decomposition of symmetric \(K3\) quartic pencils ⋮ Hasse-Witt matrices, unit roots and period integrals ⋮ Dwork hypersurfaces of degree six and Greene's hypergeometric function

Cites Work

• Isotypic decomposition of the cohomology and factorization of the zeta functions of Dwork hypersurfaces
• On the Picard-Fuchs equation and the formal Brauer group of certain elliptic \(K3\)-surfaces
• Variation of the unit root along the Dwork family of Calabi-Yau varieties
• CERTAIN VALUES OF GAUSSIAN HYPERGEOMETRIC SERIES AND A FAMILY OF ALGEBRAIC CURVES
• An explicit factorisation of the zeta functions of Dwork hypersurfaces
• ZETA-FUNCTIONS OF CERTAIN K3-FIBERED CALABI–YAU THREEFOLDS
• Formal Group Laws Arising from Algebraic Varieties

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