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In this paper we extend a result of Cowsik on set-theoretic complete intersection and a result Huneke, Morales and Goto and Nishida about Noetherian symbolic Rees algebras of ideals. As applications, we show that the symbolic Rees algebras of the fol
Externí odkaz:
http://arxiv.org/abs/2210.05886
Autor:
D'Cruz, Clare
In this survey article we give a brief history of symbolic powers and its connection with the interesting problem of set-theoretic complete intersection. We also state a few problems and conjectures. Recently, in connection to symbolic powers is the
Externí odkaz:
http://arxiv.org/abs/2003.09101
Akademický článek
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Publikováno v:
In Journal of Algebra 15 September 2023 630:317-333
Autor:
D'Cruz, Clare
Let ${\mathfrak p}$ be the defining ideal of the monomial curve ${\mathcal C}(2q+1, 2q+1+m, 2q+1+2m)$ in the affine space ${\mathbb A}_k^3$ parameterized by $(x^{2q +1}, x^{2q +1 + m}, x^{2q +1 +2 m})$ where $gcd( 2q+1,m)=1$. In this paper we compute
Externí odkaz:
http://arxiv.org/abs/1904.05797
Autor:
D'Cruz, Clare, Mandal, Mousumi
In this paper we explicitly describe the symbolic powers of curves ${\mathcal C}(q,m)$ in ${\mathbb P}^3$ parametrized by $( x^{d+2m}, x^{d+m} y^m, x^{d} y^{2m}, y^{d+2m})$, where $q,m$ are positive integers, $d=2q+1$ and $\gcd(d,m)=1$. The defining
Externí odkaz:
http://arxiv.org/abs/1904.00556
Autor:
D'Cruz, Clare
In this paper, we consider monomial curves in ${\mathbb A}_k^3$ parameterized by $t \rightarrow (t^{2q +1}, t^{2q +1 + m}, t^{2q +1 +2 m})$ where $gcd( 2q+1,m)=1$. The symbolic blowup algebras of these monomial curves is Gorenstein (\cite{goto-nis-sh
Externí odkaz:
http://arxiv.org/abs/1708.01374
Autor:
D’Cruz, Clare1 (AUTHOR) clare@cmi.ac.in, Masuti, Shreedevi K.2 (AUTHOR) shreedevi@iitdh.ac.in
Publikováno v:
Journal of Algebra & Its Applications. Sep2024, p1. 28p.
Autor:
D'Cruz, Clare, Masuti, Shreedevi K.
Let $d \geq 2$ and $m\geq 1$ be integers such that $\gcd (d,m)=1.$ Let ${\mathfrak p}$ be the defining ideal of the monomial curve in ${\mathbb A}_{ \Bbbk{k}}^d$ parametrized by $(t^{n_1}, \ldots, t^{n_d})$ where $n_i = d + (i-1)m$ for all $i = 1, \l
Externí odkaz:
http://arxiv.org/abs/1610.03658
Autor:
D'Cruz, Clare, Masuti, Shreedevi K.
In \cite{rees} Rees gave a characterization for the normal joint reduction number zero of two $\m$-primary ideals in an analytically unramified Cohen-Macaulay local ring of dimension two. Rees' result is a generalization of Zariski's product theorem
Externí odkaz:
http://arxiv.org/abs/1405.1550