Extensions of Toric Varieties

TL;DR

This paper introduces the concept of 'extensions' of toric varieties, enabling the construction of infinitely many varieties with special algebraic properties from a single example, thus advancing the understanding of their structure.

Contribution

It defines the notion of 'extension' of toric varieties and demonstrates how it can generate infinite families with desired properties, verifying Rossi's conjecture in broader contexts.

Findings

Constructs infinite families of toric varieties with specific properties

Verifies Rossi's conjecture for larger classes of toric varieties

Extends previous results in the literature on toric varieties

Abstract

In this paper, we introduce the notion of "extension" of a toric variety and study its fundamental properties. This gives rise to infinitely many toric varieties with a special property, such as being set theoretic complete intersection or arithmetically Cohen-Macaulay (Gorenstein) and having a Cohen-Macaulay tangent cone or a local ring with non-decreasing Hilbert function, from just one single example with the same property, verifying Rossi's conjecture for larger classes and extending some results appeared in literature.