Trilinear forms and Chern classes of Calabi-Yau threefolds

TL;DR

This paper explores the relationship between the trilinear form and Chern classes of Calabi-Yau threefolds, revealing numerical relations and properties depending on the form’s factorization over the reals.

Contribution

It establishes new numerical relations between the trilinear form and Chern classes of Calabi-Yau threefolds, including properties when the form has a linear factor over .

Findings

Numerical relations between Chern classes and the trilinear form.

Properties of the linear form and residual quadratic form when the cubic form has a linear factor.

Analysis of the interplay between cup product and Chern classes.

Abstract

Let X be a Calabi-Yau threefold and \mu the symmetric trilinear form on the second cohomology group H^{2}(X,\Z) defined by the cup product. We investigate the interplay between the Chern classes c_{2}(X), c_{3}(X) and the trilinear form \mu, and demonstrate some numerical relations between them. When the cubic form \mu(x,x,x) has a linear factor over \R, some properties of the linear form and the residual quadratic form are also obtained.