On maximal rational poylhedral fans
Dan Edidin, Dillon Lisk
TL;DR
This paper investigates the geometric and combinatorial properties of rational polyhedral fans with fixed rays, focusing on conditions for projectivity, completeness, and simpliciality using invariant theory techniques.
Contribution
It introduces a novel approach using invariant theory to analyze the properties of rational polyhedral fans with specified rays.
Findings
Criteria for projectivity of fans
Conditions for completeness and simpliciality
Application of invariant theory to fan classification
Abstract
In this paper we study the geometry and combinatorics of the possible rational polyhedral fans with a given set of rays. The main questions we consider are when such fans are projective, complete, or simplicial. To answer these questions we use techniques of invariant theory to characterize the quotients of maximal saturated open sets in torus representations.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Geometric and Algebraic Topology · Computational Geometry and Mesh Generation