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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…