7 citations · 7 across the 2 of their papers we have counts for
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Multiplicity sequence and integral dependence
Claudia Polini, Ngo Viet Trung, Bernd Ulrich +1
We prove that two arbitrary ideals in an equidimensional and universally catenary Noetherian local ring have the same integral closure if and only if they have the sa…
A generalization of an inequality of Lech relating multiplicity and colength
Craig Huneke, Ilya Smirnov, Javid Validashti
We study conjectured generalizations of a formula of Lech which relates the multiplicity of a finite colength ideal in an equicharacteristic local ring to its colength, and prove o…
Generalized multiplicities of edge ideals
Ali Alilooee, Ivan Soprunov, Javid Validashti
We explore connections between the generalized multiplicities of square-free monomial ideals and the combinatorial structure of the underlying hypergraphs using methods of commutat…
Hilbert-Kunz multiplicity of products of ideals
Neil Epstein, Javid Validashti
We give bounds for the Hilbert-Kunz multiplicity of the product of two ideals, and we characterize the equality in terms of the tight closures of the ideals. Connections are drawn…
On the Equality of Ordinary and Symbolic Powers of Ideals
Aline Hosry, Youngsu Kim, Javid Validashti
We consider the following question concerning the equality of ordinary and symbolic powers of ideals. In a regular local ring, if the ordinary and symbolic powers of a one-dimensio…
Syzygies and singularities of tensor product surfaces of bidegree (2,1)
Hal Schenck, Alexandra Seceleanu, Javid Validashti
Let U be a basepoint free four-dimensional subspace of the space of sections of O(2,1) on P^1 x P^1. The sections corresponding to U determine a regular map p_U: P^1 x P^1 --> P^3.…