A Note on the Formal Groups of Weighted Delsarte Threefolds

Yasuhiro Goto

Symmetry, integrability and geometry: methods and applications, Tome 14 (2018)

Résumé

One-dimensional formal groups over an algebraically closed field of positive characteristic are classified by their height. In the case of $K3$ surfaces, the height of their formal groups takes integer values between $1$ and $10$, or $\infty$. For Calabi–Yau threefolds, the height is bounded by $h^{1,2}+1$ if it is finite, where $h^{1,2}$ is a Hodge number. At present, there are only a limited number of concrete examples for explicit values or the distribution of the height. In this paper, we consider Calabi–Yau threefolds arising from weighted Delsarte threefolds in positive characteristic. We describe an algorithm for computing the height of their formal groups and carry out calculations with various Calabi–Yau threefolds of Delsarte type.

Détail

Keywords: Artin–Mazur formal groups; Calabi–Yau threefolds; weighted Delsarte varieties.

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