Primary decomposition and normality of certain determinantal ideals

TL;DR

This paper investigates the primality and primary decomposition of specific determinantal ideals generated by degree 2 polynomials, establishing their normality and contributing to algebraic geometry and commutative algebra.

Contribution

It provides new results on the primality, primary decomposition, and normality of determinantal ideals generated by quadratic polynomials.

Findings

Identified conditions under which these ideals are prime.

Established primary decomposition structures for these ideals.

Proved normality of the associated algebraic varieties.

Abstract

In this paper we study primality and primary decomposition of certain ideals which are generated by homogeneous degree $2$ polynomials and occur naturally from determinantal conditions. Normality is derived from these results.