Zaqueu Ramos
YOU?
Author Swipe
View article: Additions to a theorem of Morey-Ulrich
Additions to a theorem of Morey-Ulrich Open
Let $R = k[x_1,\ldots, x_d]$ denote a standard graded polynomial ring over an algebraically closed field $k$, and let $I \subset R$ be a perfect ideal of codimension $2$ with an $n\times (n-1)$ linear presentation matrix $ϕ$. We prove an e…
View article: Cohen--Macaulay ideals of codimension two and the geometry of plane points
Cohen--Macaulay ideals of codimension two and the geometry of plane points Open
We consider classes of codimension two Cohen--Macaulay ideals over a standard graded polynomial ring over a field. We revisit Vasconcelos' problem on $3\times 2$ matrices with homogeneous entries and describe the homological details of Ger…
View article: Matrices over polynomial rings approached by commutative algebra
Matrices over polynomial rings approached by commutative algebra Open
The main goal of the paper is the discussion of a deeper interaction between matrix theory over polynomial rings over a field and typical methods of commutative algebra and related algebraic geometry. This is intended in the sense of bring…
View article: Free divisors, blowup algebras of Jacobian ideals, and maximal analytic spread
Free divisors, blowup algebras of Jacobian ideals, and maximal analytic spread Open
Free divisors form a celebrated class of hypersurfaces which has been extensively studied in the past fifteen years. Our main goal is to introduce four new families of homogeneous free divisors and investigate central aspects of the blowup…
View article: De Jonquières transformations in arbitrary dimension. An ideal theoretic view
De Jonquières transformations in arbitrary dimension. An ideal theoretic view Open
A generalization of the plane de Jonquières transformation to arbitrary dimension is studied, with an eye for the ideal theoretic side. In particular, one considers structural properties of the corresponding base ideal and of its defining …
View article: Equigenerated ideals of analytic deviation one
Equigenerated ideals of analytic deviation one Open
The overall goal is to approach the Cohen--Macaulay property of the special fiber $\mathcal{F}(I)$ of an equigenerated homogeneous ideal $I$ in a standard graded ring over an infinite field. When the ground ring is assumed to be local, the…
View article: Equigenerated Gorenstein ideals of codimension three
Equigenerated Gorenstein ideals of codimension three Open
We focus on the structure of a homogeneous Gorenstein ideal $I$ of codimension three in a standard polynomial ring $R=\kk[x_1,\ldots,x_n]$ over a field $\kk$, assuming that $I$ is generated in a fixed degree $d$. For such an ideal $I$ this…
View article: Coordinate sections of generic Hankel matrices
Coordinate sections of generic Hankel matrices Open
One deals with degenerations by coordinate sections of the square generic Hankel matrix over a field $k$ of characteristic zero, along with its main related structures, such as the determinant of the matrix, the ideal generated by its part…
View article: Degenerations of the generic square matrix, the polar map and the determinantal structure
Degenerations of the generic square matrix, the polar map and the determinantal structure Open
One studies certain degenerations of the generic square matrix over a field [Formula: see text] along with its main related structures, such as the determinant of the matrix, the ideal generated by its partial derivatives, the polar map de…
View article: Linearly presented perfect ideals of codimension $2$ in three variables
Linearly presented perfect ideals of codimension $2$ in three variables Open
The goal of this paper is the fine structure of the ideals in the title, with emphasis on the properties of the associated Rees algebra and the special fiber. The watershed between the present approach and some of the previous work in the …
View article: Homaloidal nets and ideals of fat points II: subhomaloidal nets
Homaloidal nets and ideals of fat points II: subhomaloidal nets Open
This paper is a natural sequel to [22] in that it tackles problems of the same nature. Here one aims at the ideal theoretic and homological properties of a class of ideals of general plane fat points whose second symbolic powers hold virtu…