Varieties of minimal rational tangents on double covers of projective space

2013/03/29 by Jun-Muk Hwang, Hwang, Jun-Muk, Hosung Kim +1
Mathematics · #14J45 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.1303.7312

openalex publication_date 2013/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let ϕ: X → \mathbb Pⁿ be a double cover branched along a smooth hypersurface of degree 2m, 2 ≤ m ≤ n-1. We study the varieties of minimal rational tangents \mathcal C_x ⊂ \mathbb P T_x(X) at a general point x of X. We describe the homogeneous ideal of \mathcal C_x and show that the projective isomorphism type of \mathcal C_x varies in a maximal way as x varies over general points of X. Our description of the ideal of \mathbb C_x implies a certain rigidity property of the covering morphism ϕ. As an application of this rigidity, we show that any finite morphism between such double covers with m=n-1 must be an isomorphism. We also prove that Liouville-type extension property holds with respect to minimal rational curves on X.

Related

• Equivalence problem for minimal rational curves with isotrivial varieties of minimal rational tangents
• On the deformations of canonical double covers of minimal rational\n surfaces
• Deformations of canonical double covers
• Minimal rational curves on complete symmetric varieties
• Existence of rational curves on algebraic varieties, minimal rational tangents, and applications