Aryaman Maithani

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20242026

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math.AC2026

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…

math.AC2026

Congruence modules and Wiles defects of determinantal rings of maximal minors

Kashif Khan, Aryaman Maithani

Let $O$ be a discrete valuation ring and $A := O [X_{m \times n}] / I_{m} (X)$ the determinantal ring of maximal minors. We consider algebra maps $λ : A \to O$ , which is tantamount…

math.AC2025

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…

math.AC2025

Homological properties of invariant rings of permutation groups

Aryaman Maithani

Consider the action of a subgroup $G$ of the permutation group on the polynomial ring $S := k [x_{1}, \dots, x_{n}]$ via permutations. We show that if $k$ does not have characteris…

math.AC2025

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 $I$ has a Scarf complex, which is a subcomplex of its minimal free resolution. We say that $I$ is Scarf if its Scarf complex is also its minimal free resolutio…

math.AC2025

Edge ideals with linear quotients and without homological linear quotients

Trung Chau, Kanoy Kumar Das, Aryaman Maithani

A monomial ideal $I$ is said to have homological linear quotients if for each $k \geq 0$ , the homological shift ideal $HS_{k} (I)$ has linear quotients. It is a well-known fac…