Separable rational connectedness and weak approximation in positive characteristic

2019/07/16 by Jason Starr, Starr, Jason Michael, Zhiyu Tian +1
Computer Science · Mathematics · #14M22 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1907.07041

openalex publication_date 2019/07/16 · openalex created_date 2019/07/23 · openalex updated_date 2026/07/28

Abstract

In this short note we give a characterization of smooth projective varieties of Picard number one that are separably uniruled but not separably rationally connected. We also give a sufficient condition involving the torsion order and the uniruling index for a smooth Fano variety of Picard number one to be separably rationally connected. As an application, we prove some weak approximation results for Fano complete intersections in positive charactersitic. For example, we show that weak approximation holds at place of strong potentially good reduction for a Fano complete intersection in ℙⁿ of type (d₁, …, d_c) in characteristic p such that n>d₁+… +d_c, p>d₁, …, d_c.

Related

• Weak approximation for Fano complete intersections in positive characteristic
• Separable rational connectedness and stability
• Fano Hypersurfaces in Positive Characteristic
• Foliations and Rational Connectedness in Positive Characteristic
• Invariants of Fano varieties in families