5 papers · 1 filter
The multiplicity sequence of monomial ideals
Sudipta Das, Jonathan Montaño, Aniketh Sivakumar
We give a convex-geometric formula for the multiplicity sequence of a monomial ideal in terms of mixed volumes of polytopes constructed from its Newton polyhedron. We also construc…
Transcendental Hilbert-Kunz Multiplicities
Sudipta Das, Stephen Landsittel, Vinh Anh Pham
We prove that ordinary Hilbert-Kunz multiplicity can be transcendental. More precisely, over every uncountable algebraically closed field of characteristic , there exists a no…
Transcendental Epsilon Multiplicity via Divisor Volumes
Sudipta Das, Stephen Landsittel, Vinh Anh Pham
We prove that epsilon multiplicity can take transcendental values. The main structural result is a one-ideal formula for section rings: under natural positivity hypotheses, the eps…
Generalized Hilbert-Kunz Multiplicity for Families of Ideals
Stephen Landsittel, Sudipta Das
In this paper, we initiate a systematic study of the generalized Hilbert-Kunz multiplicity for families of ideals in a Noetherian local ring (R,m) of positive characteristic, and i…
Asymptotic colengths for families of ideals: an analytic approach
Sudipta Das, Cheng Meng
This article focuses on the existence of asymptotic colengths for families of $\fm_{R}$-primary ideals in a Noetherian local ring $(R,\fm)$. In any characteristic, we generalize gr…