A Note on the Formal Groups of Weighted Delsarte Threefolds
Yasuhiro Goto

TL;DR
This paper investigates the formal groups of weighted Delsarte Calabi-Yau threefolds in positive characteristic, providing an algorithm to compute their height and analyzing several examples to understand their distribution.
Contribution
It introduces a new algorithm for determining the height of formal groups of weighted Delsarte threefolds and applies it to various examples, expanding understanding of their properties.
Findings
Algorithm successfully computes formal group heights.
Distribution of heights varies among examples.
Provides new data on formal groups of Delsarte threefolds.
Abstract
One-dimensional formal groups over an algebraically closed field of positive characteristic are classified by their height. In the case of surfaces, the height of their formal groups takes integer values between and , or . For Calabi-Yau threefolds, the height is bounded by if it is finite, where 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.
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