6 papers
An algebraic theory of Lojasiewicz exponents
Tai Huy Ha
We develop a unified algebraic and valuative theory of Lojasiewicz exponents for pairs of graded families and filtrations of ideals. Within this framework, local Lojasiewicz expone…
Rational symbolic powers of ideals
Souvik Dey, Tai Huy Ha, Dipendranath Mahato +1
We introduce and study rational symbolic powers of ideals in Noetherian rings. We give membership criteria for rational symbolic powers and discuss settings where they agree with i…
Relative Hochster--Takayama formula and Cohen--Macaulay monomial ideal quotients
Tai Huy Ha, Nguyen Cong Minh
Hochster's and Takayama's formulas describes the multigraded components of local cohomology modules of monomial ideals in terms of simplicial complexes. In this paper, we develop a…
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…
Rational powers, invariant ideals, and the summation formula
Sankhaneel Bisui, Sudipta Das, TÃ i Huy HÃ +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…
Monomial ideals with minimal generalized Barile-Macchia resolutions
Trung Chau, Huy Tai Ha, Aryaman Maithani
We identify several classes of monomial ideals that possess minimal generalized Barile-Macchia resolutions. These classes of ideals include generic monomial ideals, monomial ideals…