arXiv subjects

S. Hamid Hassanzadeh

Publications and source records attributed to S. Hamid Hassanzadeh.

5 recordsLinked to original sources

arXiv2025

Set-Theoretically Perfect Ideals and Residual Intersections

This paper studies algebraic residual intersections in rings with Serre's condition $ S_{s} $. It demonstrates that residual intersections admit free approaches i.e. perfect subideal with the same radical. This fact leads to determining a uniform upper bound for the multiplicity of residual intersections. In positive characteristic, it follows that residual intersections are cohomologically complete intersection and, hence, their variety is connected in codimension one.

math.AC↗

arXiv2024

Bounds on the degrees of vector fields

In this article, we study the generalized Poincare problem from the opposite perspective, by establishing lower bounds on the degree of the vector field in terms of invariants of the variety.

math.AC↗

arXiv2022

RationalMaps, a package for Macaulay2

This paper describes the RationalMaps package for Macaulay2. This package provides functionality for computing several aspects of rational maps such as whether a map is birational, or a closed embedding.

math.AG↗

arXiv2017

Koszul Algebras Defined by Three Relations

This work concerns commutative algebras of the form $R=Q/I$, where $Q$ is a standard graded polynomial ring and $I$ is a homogenous ideal in $Q$. It has been proposed that when $R$ is Koszul the $i$th Betti number of $R$ over $Q$ is at most $\binom gi$, where $g$ is the number of generators of $I$; in particular, the projective dimension of $R$ over $Q$ is at most $g$. The main result of this work settles this question, in the affirmative, when $g\le 3$.

math.AC↗

arXiv2017

Bounds on the degrees of birational maps with arithmetically Cohen-Macaulay graphs

A rational map whose source and image are projectively embedded varieties has an {\em Arithmetically Cohen-Macaulay graph} if the Rees algebra of one (hence any) of its base ideals is a Cohen-Macaulay ring. If the map is birational onto the image one considers how this property forces an upper bound on the degree of a representative of the map. In the plane case a complete description is given of the Cremona maps with Cohen-Macaulay graph, while in arbitrary dimension $n$ it is shown that a Cremona map with Cohen-Macaulay graph has degree at most $n^2$.

math.AG↗