English

Groebner fan and embedded resolutions of ideals on toric varieties

Algebraic Geometry 2022-02-23 v1

Abstract

We consider the notions of Groebner fan and Newton non-degeneracy for an ideal on a toric variety, extending the two existing notions for ideals on affine spaces. We prove, without assumptions on the characteristic of the base fields, that the "Groebner fan" of such an ideal is actually a polyhedral fan and that a sub-variety defined by a Newton non-degenerate ideal on a toric variety XσX_\sigma admits a toric embedded resolution of singularities ZXσ.Z\longrightarrow X_\sigma.

Keywords

Cite

@article{arxiv.2202.10874,
  title  = {Groebner fan and embedded resolutions of ideals on toric varieties},
  author = {Fuensanta Aroca and Mirna Gómez-Morales and Hussein Mourtada},
  journal= {arXiv preprint arXiv:2202.10874},
  year   = {2022}
}