arXiv subjects

Vishal Bhatoy

Publications and source records attributed to Vishal Bhatoy.

3 recordsLinked to original sources

arXiv2026

Binomial Artin-Schelter Regular Algebras and Twisted Monoid Algebras

We study four-dimensional binomial Artin-Schelter regular algebras and their connection with twisted monoid algebras. Starting with $23$ examples up to permutation of generators, we investigate the associated monoids of I-type and the structure of their groups of fractions. We determine the corresponding finite permutation groups and compute the second group cohomology $H^2(G(M),k^\times)$. These computations allow us to construct explicit families of four-dimensional Koszul Artin-Schelter regular algebras through cocycle twists. We illustrate this construction for some of these algebras.

math.RA↗

arXiv2026

Discrete Invariants of Koszul Artin-Schelter Regular Algebras of Dimension four

We compute the superpotentials for known families of Koszul Artin-Schelter regular algebras of dimension four using Magma, and apply Schur-Weyl duality from representation theory to determine the relevant invariants. Through the Borel-Weil theorem, we interpret these invariants as sections of line bundles over partial flag varieties, resulting in geometric invariants that, in some cases, correspond to K3 surfaces. We compute discrete invariants of these geometric invariants and use them to distinguish algebras.

math.RA↗

arXiv2025

Some components of the moduli space of Koszul Artin-Schelter regular algebras of dimension four

We compute the Hochschild cohomology and the Kodaira spencer map for known families of Koszul Artin-Schelter regular algebras of dimension four. We show that when the Kodaira Spencer map at a point is a surjection, the image of the family is a component of the moduli stack of such algebras, and when the Kodaira Spencer map is a bijection, the map to the moduli stack is generically finite. We use this to identify some components of the moduli stack.

math.RA↗