Effective Non-vanishing for Algebraic Surfaces in Positive Characteristic

2005/09/05 by Qihong Xie, Xie, Qihong
Mathematics · #14E30 #14J26 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.math/0509086

openalex publication_date 2005/09/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a theorem on the effective non-vanishing problem for algebraic surfaces in positive characteristic. For the Kawamata-Viehweg vanishing, the logarithmic Kollar vanishing and the logarithmic semipositivity, we give their counterexamples on ruled surfaces in positive characteristic.

Related

• Kawamata-Viehweg Vanishing on Rational Surfaces in Positive Characteristic
• Topics in group schemes and surfaces in positive characteristic
• Counterexamples to the Kawamata-Viehweg Vanishing on Ruled Surfaces in Positive Characteristic
• On Effective Non-vanishing of Weil Divisors on Algebraic Surfaces
• Smooth rational surfaces violating Kawamata-Viehweg vanishing