Effective characterization of ordinary abelian varieties, and beyond

2025/10/22 by Jefferson Baudin, Baudin, Jefferson
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2510.19706

openalex publication_date 2025/10/22 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

We prove that the Albanese morphism of any normal proper variety X in positive characteristic satisfying S⁰(X, ω_X) ≠ 0 and P₂(X) = 1 is surjective with connected fibers, adn that Alb(X) is ordinary. We obtain from a variant of the above a purely positive characteristic proof of Chen and Hacon's effective birational characterization of complex abelian varieties.

Citations

• Generic vanishing theory in positive characteristic
• The Frobenius--stable version of the Grauert--Riemenschneider vanishing theorem fails
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• Para-abelian varieties and Albanese maps
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• The Fourier-Mukai transform made easy
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• Generic vanishing in characteristic p>0 and the characterization of ordinary abelian varieties
• Generic vanishing fails for singular varieties and in characteristic p>0
• Pluri-canonical maps of varieties of maximal Albanese dimension in positive characteristic
• An effective version of a theorem of Kawamata on the Albanese map
• Regularity on abelian varieties III: relationship with Generic Vanishing and applications
• The Picard Scheme
• Characterization of Abelian Varieties

Cited by

• On the Euler characteristic of weakly ordinary varieties of maximal Albanese dimension
• Generic vanishing theory in positive characteristic

Related

• On the Euler characteristic of weakly ordinary varieties of maximal Albanese dimension
• On algebraic fiber spaces over varieties of maximal Albanese dimension
• On the Albanese morphism of varieties with Frobenius stable Kodaira dimension zero
• On the characterization of abelian varieties for log pairs in zero and positive characteristic
• Effective characterization of semi-abelian varieties