Bounding the degrees of the defining equations of Rees rings for certain determinantal and Pfaffian ideals

2021/04/28 by Monte Cooper, Cooper, Monte, Edward F. Price +1
Mathematics · #13A30 #Advanced Topics in Algebra #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Graph theory and applications

paper · pdf · doi:10.48550/arxiv.2104.13811

openalex publication_date 2021/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider ideals of minors of a matrix, ideals of minors of a symmetric matrix, and ideals of Pfaffians of an alternating matrix. Assuming these ideals are of generic height, we characterize the condition G_s for these ideals in terms of the heights of other ideals of minors or Pfaffians of the same matrix. We additionally obtain bounds on the generation and concentration degrees of the Rees rings of a subclass of such ideals via specialization of the Rees rings in the generic case. We do this by proving, given sufficient height conditions on ideals of minors or Pfaffians of the matrix, the specialization of a resolution of the Rees ring in the generic case is an approximate resolution of the Rees ring in question. We end the paper by giving some explicit generation and concentration degree bounds.

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