On Kawamata-Viehweg Vanishing for Surfaces of del Pezzo type over imperfect fields

2025/09/22 by Bhutani, Shikha · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2509.18397

Abstract

We prove the Kawamata-Viehweg vanishing theorem for surfaces of del Pezzo type over imperfect fields of characteristic p > 5. As a consequence, we deduce the Grauert-Riemenschneider vanishing theorem for excellent divisorial log terminal threefolds whose closed points have (possibly imperfect) residue fields of positive characteristic p > 5. Finally, under this setup, we show that three-dimensional klt singularities are rational.

Citations

• On Grauert-Riemenschneider vanishing for Cohen-Macaulay schemes of klt type
• Vanishing theorems for threefolds in characteristic p>5
• Cohen-Macaulayness of absolute integral closures
• A vanishing theorem for threefolds in characteristic p>5 and applications
• On the Kawamata-Viehweg vanishing theorem for log del Pezzo surfaces in positive characteristic
• On rank one log del Pezzo surfaces in characteristic different from two and three
• On the log minimal model program for 3-folds over imperfect fields of characteristic p>5
• Vanishing theorems of Kodaira type for Witt canonical sheaves
• On the rationality of Kawamata log terminal singularities in positive\n characteristic
• Minimal model program for excellent surfaces
• Rational points on log Fano threefolds over a finite field
• A local version of the Kawamata-Viehweg vanishing theorem
• Singularities of Pairs

Cited by

• On a Grauert-Riemenschneider vanishing theorem in dimension 3

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