Trilinear forms and Chern classes of Calabi-Yau threefolds

2012/01/16 by Atsushi Kanazawa, Kanazawa, Atsushi, P. Μ. H. Wilson +1 · 2 citations
Mathematics · #14F45 #14J32 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #FOS: Physical sciences #Geometry and complex manifolds #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1201.3266

openalex publication_date 2012/01/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X be a Calabi-Yau threefold and μthe symmetric trilinear form on the second cohomology group H²(X,\Z) defined by the cup product. We investigate the interplay between the Chern classes c₂(X), c₃(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.

Cited by

• Forms and Complex Manifolds
• Stability conditions on Calabi-Yau threefolds via Brill-Noether theory of curves

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