Classification of normal toric varieties over a valuation ring of rank\n one

2013/03/08 by Walter Gubler, Alejandro Soto, Gubler, Walter +2
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1303.1987

openalex publication_date 2013/03/08 · openalex created_date 2023/01/10 · openalex updated_date 2026/07/28

Abstract

Normal toric varieties over a field or a discrete valuation ring are\nclassified by rational polyhedral fans. We generalize this classification to\nnormal toric varieties over an arbitrary valuation ring of rank one. The proof\nis based on a generalization of Sumihiro's theorem to this non-noetherian\nsetting. These toric varieties play an important role for tropicalizations.\n

Citations

• Tropical Geometry and its applications

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