English

Sparse Nullstellensatz, resultants and determinants of complexes

Algebraic Geometry 2025-06-03 v2 Commutative Algebra

Abstract

We refine and extend a result by Tuitman on the supports of a Bezout identity satisfied by a finite sequence of sparse Laurent polynomials without common zeroes in the toric variety associated to their supports. When the number of these polynomials is one more than the dimension of the ambient space, we obtain a formula for computing the sparse resultant as the determinant of a Koszul type complex.

Keywords

Cite

@article{arxiv.2407.13450,
  title  = {Sparse Nullstellensatz, resultants and determinants of complexes},
  author = {Carlos D'Andrea and Gabriela Jeronimo},
  journal= {arXiv preprint arXiv:2407.13450},
  year   = {2025}
}

Comments

23 pages, latex document. Revised version accepted for publication at International Mathematics Research Notices

R2 v1 2026-06-28T17:45:55.311Z