Vanishing theorems for toric polyhedra

2007/07/21 by Osamu Fujino, Fujino, Osamu
Mathematics · #14F17 #14F25 #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.0707.3178

openalex publication_date 2007/07/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A toric polyhedron is a reduced closed subscheme of a toric variety that are partial unions of the orbits of the torus action. We prove vanishing theorems for toric polyhedra. We also give a proof of the E₁-degeneration of Hodge to de Rham type spectral sequence for toric polyhedra in any characteristic. Finally, we give a very powerful extension theorem for ample line bundles.

Cited by

• Notes on the log minimal model program

Related

• Multiplication maps and vanishing theorems for toric varieties
• Toric sheaves and polyhedra
• Vanishing Theorems on Toric Varieties, with Erratum to a Former Paper
• Conic decomposition of a toric variety and its application to cohomology
• Vanishing Theorems on Toric Varieties in Positive Characteristic