From the 1 of 7 linked papers with an AI index.
7 papers
The variety of nilpotent matrices is -regular
Jack Jeffries, Vaibhav Pandey, Anurag K. Singh
The authors provide an elementary proof that the coordinate ring of the variety of nilpotent matrices is F‑regular and has divisor class group Z/nZ, and they show that for symmetri…
-purity and the -pure threshold as invariants of linkage
Vaibhav Pandey
The generic link of an unmixed radical ideal is a prime ideal. We show that the squarefreeness of the initial ideal and -purity are, however, not preserved along generic links.…
Bounds on the plus-pure thresholds of some hypersurfaces in (ramified) regular rings
Marta Benozzo, Vignesh Jagathese, Vaibhav Pandey +3
We study the plus-pure threshold (ppt) of hypersurfaces in mixed characteristic. We show that the ppt limits to the -pure threshold (fpt) as we ramify the base DVR. Additionally…
The arithmetic rank of the residual intersections of a complete intersection ideal
Manav Batavia, Kesavan Mohana Sundaram, Vaibhav Pandey +1
The arithmetic rank of an ideal in a polynomial ring over an algebraically closed field is the smallest number of equations needed to define its vanishing locus set-theoretically.…
Symbolic powers of the generic linkage of maximal minors
Vaibhav Pandey, Matteo Varbaro
Let be the ideal generated by the maximal minors of a matrix of indeterminates over a field and let denote the generic link, i.e., the most general link, of . The genera…
The arithmetic rank of determinantal nullcones
Jack Jeffries, Vaibhav Pandey, Anurag K. Singh +1
We compute the arithmetic rank as well as the local/étale cohomological dimension of nullcone ideals arising from the classical actions of the symplectic group, the general linear…