English

Graphs and Ideals generated by some 2-minors

Commutative Algebra 2009-11-16 v1

Abstract

Let G be a finite graph on [n] = {1,2,3,...,n}, X a 2 times n matrix of indeterminates over a field K, and S = K[X] a polynomial ring over K. In this paper, we study about ideals I_G of S generated by 2-minors [i,j] of X which correspond to edges {i,j} of G. In particular, we construct a Groebner basis of I_G as a set of paths of G and compute a primary decomposition.

Keywords

Cite

@article{arxiv.0911.2549,
  title  = {Graphs and Ideals generated by some 2-minors},
  author = {Masahiro Ohtani},
  journal= {arXiv preprint arXiv:0911.2549},
  year   = {2009}
}

Comments

14 pages, to appear in Communications in Algebra

R2 v1 2026-06-21T14:11:05.650Z