Degeneracy of triality-symmetric morphisms

TL;DR

This paper introduces triality symmetry for vector bundle morphisms, derives Chern class formulas for their degeneracy loci, and links rank 2 bundles to octonion algebra bundles, expanding geometric symmetry understanding.

Contribution

It defines triality symmetry for morphisms, computes associated degeneracy locus formulas, and connects rank 2 bundles with octonion algebra bundles, offering new geometric insights.

Findings

Derived Chern class formulas for triality-symmetric degeneracy loci

Established a canonical association between rank 2 bundles and octonion algebra bundles

Expanded the understanding of symmetries in vector bundle morphisms

Abstract

We define a new symmetry for morphisms of vector bundles, called triality symmetry, and compute Chern class formulas for the degeneracy loci of such morphisms. In an appendix, we show how to canonically associate an octonion algebra bundle to any rank 2 vector bundle.