Vivek Mukundan

activity

20152025

most citedRees Algebras and Almost Linearly Presented Ideals

20 citations · 62 across the 16 of their papers we have counts for

collaborators

19 papers

math.AC2025

Optimal Parametrizations and Valuations

Reinhold Hübl, Craig Huneke, Sarasij Maitra +1

This article discusses a way for uniquely setting up the valuations for the minimal generators of the maximal ideal of a one dimensional complete reduced and irreducible local alge…

math.AC2024

Symbolic Powers of Classical Varieties

Arvind Kumar, Vivek Mukundan

Let $R = K [x_{1}, \dots, x_{n}]$ and let $a_{1}, \dots, a_{m}$ be homogeneous ideals satisfying certain properties, which include a description of the Noetherian s…

math.AC2024

Two Criteria For Quasihomogeneity

Sarasij Maitra, Vivek Mukundan

Let $(R, m_{R}, k)$ be a one-dimensional complete local reduced $k$ -algebra over a field of characteristic zero. The ring $R$ is said to be quasihomogeneous if there exists…

math.AC2023

Computing mixed multiplicities, mixed volumes, and sectional Milnor numbers

Kriti Goel, Vivek Mukundan, Sudeshna Roy +1

This is an expository version of our paper [arXiv:1902.07384]. Our aim is to present recent Macaulay2 algorithms for computation of mixed multiplicities of ideals in a Noetherian r…

math.AC2023

Extremal behavior of reduced type of one dimensional rings

Sarasij Maitra, Vivek Mukundan

Let $R$ be a domain that is a complete local $k$ algebra in dimension one. In an effort to address the Berger's conjecture, a crucial invariant reduced type $s (R)$ was int…

math.AC2022★ 2 cited

Valuations and Nonzero Torsion in Module of Differentials

Sarasij Maitra, Vivek Mukundan

Let $(R, m_{R}, k)$ be a one-dimensional complete local reduced $k$ -algebra over a field of characteristic zero. R. Berger conjectured that $R$ is regular if and only if the…

math.AC2022★ 8 cited

Torsion in Differentials and Berger's Conjecture

Craig Huneke, Sarasij Maitra, Vivek Mukundan

Let $(R, m, k)$ be an equicharacteristic one-dimensional complete local domain over an algebraically closed field $k$ of characteristic 0. R. Berger conj…

math.AC2021★ 1 cited

On the resurgence and asymptotic resurgence of homogeneous ideals

A. V. Jayanthan, Arvind Kumar, Vivek Mukundan

Let $K$ be a field and $R = K [x_{1}, \dots, x_{n}]$ . We obtain an improved upper bound for asymptotic resurgence of squarefree monomial ideals in $R$ . We study the e…

math.AC2021

Tight closure of powers of parameter ideals in hypersurface rings and their tight Hilbert polynomials

Saipriya Dubey, Vivek Mukundan, Jugal Verma

In this paper we find the tight closure of powers of parameter ideals of certain diagonal hypersurface rings. In many cases the associated graded ring with respect to tight closure…

math.AC2020

Expected resurgence of ideals defining Gorenstein rings

Eloísa Grifo, Craig Huneke, Vivek Mukundan

Building on previous work by the same authors, we show that certain ideals defining Gorenstein rings have expected resurgence, and thus satisfy the stable Harbourne Conjecture. In…

math.AC2019

Multiplicity of the saturated special fiber ring of height three Gorenstein ideals

Yairon Cid-Ruiz, Vivek Mukundan

Let $R$ be a polynomial ring over a field and $I \subset R$ be a Gorenstein ideal of height three that is minimally generated by homogeneous polynomials of the same degree. We comp…

math.AC2019★ 16 cited

Expected resurgences and symbolic powers of ideals

Eloísa Grifo, Craig Huneke, Vivek Mukundan

We give explicit criteria that imply the resurgence of a self-radical ideal in a regular ring is strictly smaller than its codimension, which in turn implies that the stable versio…

math.AC2019★ 3 cited

Algorithms for computing mixed multiplicities, mixed volumes and sectional Milnor numbers

Kriti Goel, Vivek Mukundan, Sudeshna Roy +1

We present a package 'MixedMultiplicity' for computing mixed multiplicities of ideals in a Noetherian ring which is either local or a standard graded algebra over a field. This ena…

math.AC2019★ 1 cited

On the Vanishing of the normal Hilbert coefficients of ideals

Kriti Goel, Vivek Mukundan, J. K. Verma

Using vanishing of graded components of local cohomology modules of the Rees algebra of the normal filtration of an ideal, we give bounds on the normal reduction number. This helps…

math.AC2019

Diagonal Subalgebras of Residual Intersections

H. Ananthnarayan, Neeraj Kumar, Vivek Mukundan

Let $k$ be a field, $S$ be a bigraded $k$ -algebra, and $S_{Δ}$ denote the diagonal subalgebra of $S$ corresponding to $Δ = {(cs, es) ∣ s \in Z}$ . It is k…

math.AC2018★ 11 cited

Tight Closure of powers of ideals and tight Hilbert polynomials

Kriti Goel, Vivek Mukundan, J. K. Verma

Let $(R, m)$ be an analytically unramified local ring of positive prime characteristic $p .$ For an ideal $I$ , let $I^{*}$ denote its tight closure. We introduce the tight Hi…

math.AC2018

Equations defining certain graphs

Youngsu Kim, Vivek Mukundan

Consider the rational map $ϕ : P_{k}^{n - 1} ⟶ [f_{0} : \dots : f_{n}] P_{k}^{n}$ defined by homogeneous polynomials $f_0,\dots,f…

math.AC2016

Detecting Koszulness and related homological properties from the algebra structure of Koszul homology

Amanda Croll, Roger Dellaca, Anjan Gupta +6

Let $k$ be a field and $R$ a standard graded $k$ -algebra. We denote by $H^{R}$ the homology algebra of the Koszul complex on a minimal set of generators of the irrelev…

math.AC2015★ 20 cited

Rees Algebras and Almost Linearly Presented Ideals

Jacob A. Boswell, Vivek Mukundan

Consider a grade 2 perfect ideal $I$ in $R = k [x_{1}, \dots, x_{d}]$ which is generated by forms of the same degree. Assume that the presentation matrix $φ$ is almost linear, that is, all…