ASL structures of some quadrics

Joydip Saha; Indranath Sengupta

paper

ASL structures of some quadrics

arXiv:2104.14772

Abstract

Let $K$ be a field and $X$ , $Y$ denote matrices such that, the entries of $X$ are either indeterminates over $K$ or $0$ and the entries of $Y$ are indeterminates over $K$ which are different from those appearing in $X$ . We consider ideals of the form $I_{1} (X Y)$ , which is the ideal generated by the $1 \times 1$ minors of the matrix $X Y$ . We prove that the quotient ring $K [X, Y] / I_{1} (X Y)$ admits an ASL structure for certain $X$ and $Y$ .