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New versions of Frobenius and integral closure of ideals
Kriti Goel, Kyle Maddox, William D. Taylor
In this article, we define three new operations on ideals which generalize integral closure and Frobenius closure of ideals, whose definitions incorporate an auxiliary ideal and a…
On the Hilbert-Samuel coefficients of Frobenius powers of an ideal
Arindam Banerjee, Kriti Goel, J. K. Verma
We provide suitable conditions under which the asymptotic limit of the Hilbert-Samuel coefficients of the Frobenius powers of an -primary ideal exists in a Noetherian…
Generalized Hilbert-Kunz function of the Rees algebra of the face ring of a simplicial complex
Arindam Banerjee, Kriti Goel, J. K. Verma
Let be the face ring of a simplicial complex of dimension and be the Rees algebra of the maximal homogeneous ideal of We…
Hilbert-Kunz function and Hilbert-Kunz multiplicity of some ideals of the Rees algebra
Kriti Goel, Mitra Koley, J. K. Verma
We prove that the Hilbert-Kunz function of the ideal of the Rees algebra , where is an -primary ideal of a -dimensional local ring $(R…
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…
The Minkowski equality and inequality for multiplicity of ideals
Kriti Goel, R. V. Gurjar, J. K. Verma
In this exposition of the equality and inequality of Minkowski for multiplicity of ideals, we provide simple algebraic and geometric proofs. Connections with mixed multiplicities o…