Fibers of Projections and Submodules of Deformations

2009/11/19 by Roya Beheshti, David Eisenbud, Beheshti, Roya +1
Computer Science · Engineering · Mathematics · #13B22 #14B07 #14N05 #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AC #math.AG #msc:13B22 #msc:14B07 #msc:14N05

paper · pdf · doi:10.48550/arxiv.0911.3924

arxiv created 2009/11/19 · openalex publication_date 2009/11/19 · arxiv updated 2009/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We bound the complexity of the fibers of the generic linear projection of a smooth variety in terms of a new family of invariants. These invariants are closely related to ideas of John Mather, and we give a simple proof of his bound on the Thom-Boardman invariants of a generic projection as an application.

Related

• The theorem of Mather on generic projections for singular varieties
• Fibres of embedding dimension 2 in generic projections
• Deformation theory from the point of view of fibered categories
• A bound on embedding dimensions of geometric generic fibers
• Non-simple abelian varieties in a family: arithmetic approaches