1 citations · 1 across the 11 of their papers we have counts for
12 papers
On the -invariant of a normal graded ring
Aryaman Maithani, Anurag K. Singh, Kei-ichi Watanabe
The -invariant of a normal graded ring was defined recently by Okuma, Watanabe, and Yoshida. We study this for invariant rings of finite groups, proving that it is nonpositive i…
The arithmetic rank of nullcones of classical invariant rings
Manav Batavia, Aryaman Maithani, Kesavan Mohana Sundaram
We compute the arithmetic rank of nullcone ideals arising from natural actions of the special linear, orthogonal, and symplectic groups on direct sums of copies of their standard a…
Congruence modules and Wiles defects of determinantal rings of maximal minors
Kashif Khan, Aryaman Maithani
Let be a discrete valuation ring and the determinantal ring of maximal minors. We consider algebra maps , which is tantamount…
Abelian extensions of equicharacteristic regular rings need not be Cohen-Macaulay
Aryaman Maithani, Anurag K. Singh, Prashanth Sridhar
By a theorem of Roberts, the integral closure of a regular local ring in a finite abelian extension of its fraction field is Cohen-Macaulay, provided that the degree of the extensi…
Homological properties of invariant rings of permutation groups
Aryaman Maithani
Consider the action of a subgroup of the permutation group on the polynomial ring via permutations. We show that if does not have characteris…
The Scarf complex of squarefree powers, symbolic powers of edge ideals, and cover ideals of graphs
Trung Chau, Nursel Erey, Aryaman Maithani
Every monomial ideal has a Scarf complex, which is a subcomplex of its minimal free resolution. We say that is Scarf if its Scarf complex is also its minimal free resolutio…
Edge ideals with linear quotients and without homological linear quotients
Trung Chau, Kanoy Kumar Das, Aryaman Maithani
A monomial ideal is said to have homological linear quotients if for each , the homological shift ideal has linear quotients. It is a well-known fac…
Polynomial invariants of classical subgroups of : Conjugation over finite fields
Aryaman Maithani
Consider the conjugation action of the general linear group on the polynomial ring . When is an infinite field, the ring of invari…
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…
Splitting the difference: Computations of the Reynolds operator in classical invariant theory
Aryaman Maithani
If is a linearly reductive group acting rationally on a polynomial ring , then the inclusion possesses a unique -equivariant splitting, called t…
Minimal cellular resolutions of powers of graphs
Trung Chau, Tài Huy Hà, Aryaman Maithani
Let be a connected graph and let denote its edge ideal. We classify when , for , admits a minimal Lyubeznik resolution. We also give a characterization…
Linear quotients of connected ideals of graphs
H. Ananthnarayan, Omkar Javadekar, Aryaman Maithani
As a higher analogue of the edge ideal of a graph, we study the -connected ideal . This is the monomial ideal generated by the connected subsets of size $t…