English

On ideals generated by two generic quadratic forms in the exterior algebra

Commutative Algebra 2019-07-08 v1 Combinatorics

Abstract

Based on the structure theory of pairs of skew-symmetric matrices, we give a conjecture for the Hilbert series of the exterior algebra modulo the ideal generated by two generic quadratic forms. We show that the conjectured series is an upper bound in the coefficient-wise sense, and we determine a majority of the coefficients. We also conjecture that the series is equal to the series of the squarefree polynomial ring modulo the ideal generated by the squares of two generic linear forms.

Keywords

Cite

@article{arxiv.1803.08918,
  title  = {On ideals generated by two generic quadratic forms in the exterior algebra},
  author = {Veronica Crispin Quiñonez and Samuel Lundqvist and Gleb Nenashev},
  journal= {arXiv preprint arXiv:1803.08918},
  year   = {2019}
}

Comments

15 pages, 1 figure

R2 v1 2026-06-23T01:03:25.833Z