Anurag K. Singh

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math.AC2026

The variety of nilpotent matrices is $F$ -regular

Jack Jeffries, Vaibhav Pandey, Anurag K. Singh

We give an elementary proof that the coordinate ring of the variety of nilpotent matrices is $F$ -regular; over an infinite field $K$ , this ring also arises as the nullcone for the…

math.AC2023

Flat morphisms with regular fibers do not preserve $F$ -rationality

Eamon Quinlan-Gallego, Austyn Simpson, Anurag K. Singh

For each positive prime integer $p$ we construct a standard graded $F$ -rational ring $R$ , over a field $K$ of characteristic $p$ , such that $R \otimes_{K} K$ is not $F$ -rati…

math.AC2023

Local cohomology of modular invariant rings

Kriti Goel, Jack Jeffries, Anurag K. Singh

For $K$ a field, consider a finite subgroup $G$ of $GL_{n} (K)$ with its natural action on the polynomial ring $R := K [x_{1}, \dots, x_{n}]$ . Let $n$ denote the homo…

The variety of nilpotent matrices is F-regular

Flat morphisms with regular fibers do not preserve F-rationality

Local cohomology of modular invariant rings

The variety of nilpotent matrices is $F$ -regular

Flat morphisms with regular fibers do not preserve $F$ -rationality