9 papers
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…
Analytic Spread via Linear Matroids
Stephen Landsittel, Eran Nevo
We give a systematic analysis of the analytic spread of the determinantal ideal arising from a pair of graphs . We give sharp bounds for this analytic spread, and…
Some Remarks About Saturation of Ideals
Souvik Dey, Stephen Landsittel
In this paper we observe when saturation of ideals in a local ring R commutes with extension along ring maps and initial ideals. We give a characterization in terms of Cohen Macaul…
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…
Composite Linear Quotient Orderings of Ideals and Modified Anticycles
Stephen Landsittel
In this paper we give a construction for a linear quotient ordering of a class of products of two ideals which have linear quotients. We apply this construction to give a class of…
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…
Analytic spread of binomial edge ideals
Eduardo Camps-Moreno, Deblina Dey, Souvik Dey +5
We investigate the analytic spread of binomial edge ideals of finite simple graphs. We provide tight bounds for this invariant in general. For special families of graphs (e.g., clo…
Some Formulas for Epsilon Multiplicity in Local Rings
Stephen Landsittel
We prove that the epsilon multiplicity exists in a Noetherian local ring whenever the nildradical of the completion of R has nonmaximal dimension. We also extend the volume equals…
Epsilon multiplicity is a limit of Amao multiplicities
Steven Dale Cutkosky, Stephen Landsittel
In this paper we prove a volume = multiplicity type theorem for epsilon multiplicity. We show that epsilon multiplicity is a limit of Amao multiplicities.