Trilinear forms and Chern classes of Calabi-Yau threefolds

Abstract

Let X be a Calabi-Yau threefold and μthe 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 μ, and demonstrate some numerical relations between them. When the cubic form μ(x,x,x) has a linear factor over \R, some properties of the linear form and the residual quadratic form are also obtained.

to appear in Osaka Journal of Mathematics