10 papers · 1 filter
The variety of nilpotent matrices is -regular
Jack Jeffries, Vaibhav Pandey, Anurag K. Singh
We give an elementary proof that the coordinate ring of the variety of nilpotent matrices is -regular; over an infinite field , this ring also arises as the nullcone for the…
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.…
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…
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…
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…
-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.…
On the natural nullcones of the symplectic and general linear groups
Vaibhav Pandey, Yevgeniya Tarasova, Uli Walther
Consider a group acting on a polynomial ring S over a field K by degree-preserving K-algebra automorphisms. Several key properties of the invariant ring can be deduced by studying…
Counting geometric branches via the Frobenius map and -nilpotent singularities
Hailong Dao, Kyle Maddox, Vaibhav Pandey
We give an explicit formula to count the number of geometric branches of a curve in positive characteristic using the theory of tight closure. This formula readily shows that the p…
Linkage and -Regularity of Determinantal Rings
Vaibhav Pandey, Yevgeniya Tarasova
In this paper, we prove that the generic link of a generic determinantal ring defined by maximal minors is strongly -regular. In the process, we strengthen a result of Chardin a…
When are the natural embeddings of classical invariant rings pure?
Melvin Hochster, Jack Jeffries, Vaibhav Pandey +1
Consider a reductive linear algebraic group acting linearly on a polynomial ring over an infinite field; key examples are the general linear group, the symplectic group, th…