8 papers
Boundedness of geometrically integral -klt del Pezzo surfaces
Shikha Bhutani, Sudipta Das
We prove the remaining positive characteristic cases of the Borisov-Alexeev-Borisov conjecture for geometrically integral -klt del Pezzo surfaces over arbitrary fields…
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…
Rational powers, invariant ideals, and the summation formula
Sankhaneel Bisui, Sudipta Das, Tài Huy Hà +1
We provide explicit descriptions for the rational powers and Rees valuations of several classes of ideals invariant under natural actions of tori and products of general linear gro…
A Volume = Multiplicity formula for -families of ideals
Sudipta Das
In this paper, we work with certain families of ideals called -families in rings of prime characteristic. This family of ideals is present in the theories of tight closure, Hilb…