On the generic degree of two-parameter period mappings

TL;DR

This paper introduces a method to compute the generic degree of period maps on quasi-projective surfaces and applies it to Calabi-Yau 3-folds, confirming the generic Torelli theorem for these cases.

Contribution

It provides a new computational approach for the generic degree of period maps and explicitly applies it to Calabi-Yau 3-folds from toric hypersurfaces, establishing the Torelli theorem.

Findings

Computed the generic degree for three Calabi-Yau 3-fold families

Confirmed the generic Torelli theorem for these families

Developed a new method for period map degree calculation

Abstract

We present a method for computing the generic degree of a period map defined on a quasi-projective surface. As an application, we explicitly compute the generic degree of three period maps underlying families of Calabi-Yau 3-folds coming from toric hypersurfaces. As a consequence, we show that the generic Torelli theorem holds for these cases.