English

Graded basic elements

Algebraic Geometry 2020-06-02 v3 Commutative Algebra

Abstract

We prove the existence theorem for basic elements in the quasi-projective case, extending results of Eisenbud-Evans and Bruns from the affine case. We give several geometric applications. For example, we show that every local complete intersection of pure codimension two in a smooth projective variety of dimension d over an infinite field is the degeneracy locus of d-1 sections of a rank d bundle.

Keywords

Cite

@article{arxiv.1911.10646,
  title  = {Graded basic elements},
  author = {Mengyuan Zhang},
  journal= {arXiv preprint arXiv:1911.10646},
  year   = {2020}
}

Comments

13 pages, revised version

R2 v1 2026-06-23T12:25:46.593Z