Anurag K. Singh

collaborators

4 papers

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.CO2023

Subsequence frequency in binary words

Krishna Menon, Anurag Singh

The numbers we study in this paper are of the form $B_{n, p} (k)$ , which is the number of binary words of length $n$ that contain the word $p$ (as a subsequence) exactly $k$ times.…

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

Subsequence frequency in binary words

Local cohomology of modular invariant rings

The variety of nilpotent matrices is $F$ -regular

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