On degenerate sections of vector bundles

2017/03/30 by Tseng, Dennis
#14C05 #14C35 #14J60 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1703.10568

Abstract

We consider the locus of sections of a vector bundle on a projective scheme that vanish in higher dimension than expected. We show that after applying a high enough twist, any maximal component of this locus consists entirely of sections vanishing along a subscheme of minimal degree. In fact, we will give a more refined description of this locus, which will allow us to deduce its limit in the Grothendieck ring of varieties.

Related

• Cayley-Bacharach theorems with excess vanishing
• Some results on deformations of sections of vector bundles
• Ample vector bundles with sections vanishing on special varieties
• Nonemptiness of symmetric degeneracy loci
• Residual intersection theory with reducible schemes