TL;DR
This paper explores the geometric properties of toric schemes constructed from monoid algebras, analyzing how their structure depends on the base scheme's geometry, with implications for properties like normality, dimension, and Serre's conditions.
Contribution
It provides a comprehensive study of the geometric features of toric schemes over arbitrary bases, linking their properties to the base scheme's geometry.
Findings
Characterization of separation and finiteness properties
Analysis of irreducibility, normality, and catenarity
Influence of base scheme's geometry on toric schemes
Abstract
Geometric properties of schemes obtained by gluing algebras of monoids, including separation and finiteness properties, irreducibility, normality, catenarity, dimension, and Serre's properties (S_k) and (R_k), are investigated. This is used to show how the geometry of a toric scheme over an arbitrary base is influenced by the geometry of the base.
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