Purely Algebraic Method to Construct Toric Schemes

Details Purely Algebraic Method to Construct Toric Schemes Purely Algebraic Method to Construct Toric Schemes

2007-11-04

arxiv.org/abs/0711.0522v2

Mathematics

Algebraic Geometry

13 pages

Scientific paper

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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