Author

Anurag K. Singh

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Preprint Oct 2026

On an ideal membership problem

Suppose $f_1, \dots, f_{n+1}$ are elements of a regular ring $R$, where $n := \dim R$. The first author proved that $f_1^n \cdots f_{n+1}^n \in (f_1^{n+1}, \dots, f_{n+1}^{n+1})R$; this uses the Brian\c con-Skoda theorem --- no simpler proof is known, as far as we are aware. We show here that this result is optimal in...

Melvin Hochster, J. Jeffries, KC Nawaj et al. · 0 citations

Preprint Jul 2026

The variety of nilpotent matrices is $F$-regular

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 conjugation action of the general linear group $\textrm{GL}_n(K)$ on the polynomial ring $K[X]$, where $X$ is an $n\times n$ matrix of indet...

J. Jeffries, Vaibhav Pandey, Anurag K. Singh · 0 citations