Ideals of adjacent minors
By Serkan Hoşten, Seth Sullivant. 2003
56 citations recorded by the source corpus.
We give a description of the minimal primes of the ideal generated by the 2×2 adjacent minors of a generic matrix. We also compute the complete prime decomposition of the ideal of adjacent m×m minors of an m×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.
Subfields: Algebra and Number Theory
View Paper: https://www.semanticscholar.org/paper/7828fbf669964d90a5fcebd97b687fec4ca304a5
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In Algebra and Number Theory
Citations in the corpus
- Graphs and Ideals Generated by Some 2-Minors (2009, background): “Hoşten and Sullivant [7] studied ideals of adjacent minors as a generalization of ideals of Diaconis, Eisenbud, and Sturmfels.”
- IDEALS GENERATED BY 2-MINORS, COLLECTIONS OF CELLS AND STACK POLYOMINOES (2012, unknown): “Motivated by applications in algebraic statistics, ideals generated by even more general sets of minors have been investigated, including ideals generated by adjacent 2-minors, see [7,5,9], or ideals generated by an arbitrary set of 2-minors in an 2 × n-matrix [4].”