Fano varieties with large Seshadri constants in positive characteristic

2017/07/10 by Ziquan Zhuang, Zhuang, Ziquan
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1707.02682

openalex publication_date 2017/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that a Fano variety (with arbitrary singularities) of dimension n in positive characteristic is isomorphic to ℙⁿ if the Seshadri constant of the anti-canonical divisor at some smooth point is greater than n and classify Fano varieties whose anti-canonical divisors have Seshadri constants n. In characteristic p>5 and dimension 3, we also show that Fano varieties X with Seshadri constants ε(-K_X,x)>2+ε at some smooth point x∈ X (for some fixed ε>0) have bounded anti-canonical degrees.

Related

• Weak boundedness of Fano threefolds with large Seshadri constants in characteristic p>5
• Seshadri constants of the anticanonical divisors of Fano manifolds with large index
• Seshadri constants and degrees of defining polynomials
• Fano varieties with high degree
• Fano symmetric varieties with low rank