Ideals of Adjacent Minors
Serkan Hosten, Seth Sullivant
Abstract
We give a description of the minimal primes of the ideal generated by the 2 x 2 adjacent minors of a generic matrix. We also compute the complete prime decomposition of the ideal of adjacent m x m minors of an m x n generic matrix when the characteristic of the ground field is zero. A key intermediate result is the proof that the ideals which appear as minimal primes are, in fact, prime ideals. This introduces a large new class of mixed determinantal ideals that are prime.
Create a lesson
Related papers
On the Stable category of maximal Cohen-Macaulay modules over Gorenstein rings-II
Tony J. Puthenpurakal
Symbolic powers of the ideal ofn general points in Pn-1
Ralf Fröberg, Boris Shapiro
Density functions for filtrations of graded ideals
Suprajo Das, Hoang Le Truong
Finitistic injective dimension exceeding finitistic projective dimension for a commutative ring
Liang Chen
A criterion for determinantal presentations of numerical semigroup rings
Satoshi Murai, Kou Takahashi
Normality of ideals beyond the standard graded setting: families from numerical semigroup rings
Naoyuki Matsuoka