Restricted classes of Veronese type ideals and algebras

TL;DR

This paper investigates specific classes of monomial ideals related to Veronese ideals, focusing on their algebraic properties, powers, and fiber cones, with emphasis on bounded support and spread conditions.

Contribution

It introduces and analyzes $c$-bounded $t$-spread Veronese ideals and Veronese ideals of bounded support, exploring their algebraic structures and properties.

Findings

Characterization of $c$-bounded $t$-spread Veronese ideals

Analysis of powers and fiber cones of these ideals

Insights into algebraic properties of bounded support Veronese ideals

Abstract

We study ideals which are generated by monomials of degree $d$ in the polynomial ring in $n$ variables and which satisfy certain numerical side conditions regarding their exponents. Typical examples of such ideals are the ideals of Veronese type, squarefree Veronese ideals or $t$-spread Veronese ideals. In this paper we focus on $c$-bounded $t$-spread Veronese ideals and on Veronese ideals of bounded support. Their powers as well as their fiber cone is also be considered.