A Note on the Formal Groups of Weighted Delsarte Threefolds

Abstract

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 ∞. For Calabi-Yau threefolds, the height is bounded by h¹'² + 1 if it is finite, where h¹'² 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.