Degeneration of Dual Varieties of Hypersurfaces

2023/12/29 by Yilong Zhang, Zhang, Yilong
Mathematics · #14D06 #14J70 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2312.17728

openalex publication_date 2023/12/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Consider a one-parameter family of smooth projective varieties X_t which degenerate into a simple normal crossing divisor at t=0. What is the dual variety in the limit? We answer this question for a hypersurface of degree d degenerate to the union of two hypersurfaces of degree d₁ and d-d₁ meeting transversely. We find all the irreducible components of the dual variety in the limit and their multiplicities.

Related

• Degenerating Discriminants
• Extremal degenerations of polarized Hodge structures
• Regularity in Linear Degenerations of Flag Variety
• Semi-Stable Degeneration of Toric Varieties and Their Hypersurfaces
• Degenerations of Rationally Connected Varieties