Purely Algebraic Method to Construct Toric Schemes

2007/11/04 by Ting Li, Li, Ting
Computer Science · Mathematics · #14M25 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AG #msc:14M25

paper · pdf · doi:10.48550/arxiv.0711.0522

13 pages

openalex publication_date 2007/11/04 · arxiv created 2007/12/01 · arxiv updated 2011/11/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we first give some elementary proprieties of monoids and fans, then construct a toric scheme over an arbitrary ring, from a given fan. Using Valuative Criterion, we prove that this scheme is separated and give the sufficient and necessary condition when it is proper. We also study the regularity and logarithmic regularity of it. Finally we study the morphisms of toric schemes induced by the homomorphisms of fans.

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