10 papers
Optimal Lojasiewicz-Simon Exponents and the Intrinsic Singularities of Analytic Functionals
Tewodros Amdeberhan, Tai Huy Ha
We prove that the optimal Lojasiewicz--Simon exponent of a real-analytic functional on a Banach space is an intrinsic invariant of its finite-dimensional Lyapunov--Schmidt singular…
Cohen-Macaulay higher conormal and Kähler differential modules of squarefree monomial ideals
Tài Huy Hà, Nguyen Cong Minh
Let and let be a nonzero squarefree monomial ideal. Motivated by the classical higher-order Kähler differential modules and by the theory…
Frobenius dilation of Hilbert function, Demailly's conjecture, and varieties of powers
Trung Hoa Dinh, Tai Huy Ha
We prove a Frobenius-dilation inequality for Hilbert functions of ideals generated by powers of fixed homogeneous forms in characteristic zero. Via Emsalem--Iarrobino inverse syste…
Polynomial interpolation and the Waldschmidt constant of points in projective space
Tài Huy Hà, Aniketh Sivakumar
We establish Chudnovsky's Conjecture and, more generally, Demailly's Conjecture for any finite set of points in , where is an algebraically closed field of char…
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…
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…
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…
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…
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…
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…