11 papers
Symbolic Powers and Asymptotic Invariants of GL-Invariant Ideals
Sankhaneel Bisui, Alexandra Seceleanu
This work concerns ideals invariant under the action of the group of linear base changes on a generic matrix; we call these GL-invariant ideals. We determine the ordinary powers, t…
Symbolic powers via extension
Sankhaneel Bisui, Haoxi Hu
This article investigates under which conditions the symbolic powers of the extension of an ideal is the same as the extension of the symbolic powers. Our result generalizes the kn…
Demailly's Conjecture for general and very general points
Sankhaneel Bisui, Dipendranath Mahato
We prove that at least , where , many general points, satisfy Demailly's conjecture. Previously, it was known to be true f…
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…
Lower bounds for Waldschmidt constants and Demailly's Conjecture for general and very general points
Sankhaneel Bisui, Thai Thanh Nguyen
We prove Demailly's Conjecture concerning the lower bound for the Waldschmidt constant in terms of the initial degree of the second symbolic powers for any set of generic points or…
Chudnovsky's Conjecture and the stable Harbourne-Huneke containment for general points
Sankhaneel Bisui, Thái Thành Nguyên
In our previous work with Grifo and Hà, we showed the stable Harbourne-Huneke containment and Chudnovsky's conjecture for the defining ideal of sufficiently many general points in…
RandomPoints package for Macaulay2
Sankhaneel Bisui, Zhan Jiang, Sarasij Maitra +2
We present {\tt RandomPoints}, a package in \emph{Macaulay2} designed mainly to identify rational and geometric points in a variety over a finite field. We provide tools to estimat…
Demailly's Conjecture and the Containment Problem
Sankhaneel Bisui, Eloísa Grifo, Huy Tài Hà +1
We investigate Demailly's Conjecture for a general set of sufficiently many points. Demailly's Conjecture generalizes Chudnovsky's Conjecture in providing a lower bound for the Wal…
Chudnovsky's Conjecture and the stable Harbourne-Huneke containment
Sankhaneel Bisui, Eloísa Grifo, Huy Tài Hà +1
In this paper, we investigate containment statements between symbolic and ordinary powers and bounds on the Waldschmidt constant of defining ideals of points in projective spaces.…
Fiber invariants of projective morphisms and regularity of powers of ideals
Sankhaneel Bisui, Huy Tai Ha, Abu Chackalamannil Thomas
We introduce an invariant, associated to a coherent sheaf over a projective morphism of schemes, which controls when sheaf cohomology can be passed through the given morphism. We t…
Resurgence numbers of fiber products of projective schemes
Sankhaneel Bisui, Huy Tai Ha, A. V. Jayanthan +1
We investigate the resurgence and asymptotic resurgence numbers of fiber products of projective schemes. Particularly, we show that while the asymptotic resurgence number of the k-…