English

Biliaison of sheaves

Algebraic Geometry 2020-04-10 v2 Commutative Algebra

Abstract

We define an equivalence relation among coherent sheaves on a projective variety called biliaison. We prove the existence of sheaves that are minimal in a biliaison class in a suitable sense, and show that all sheaves in the same class can be obtained from a minimal one using certain deformations and other basic moves. Our results generalize the main theorems of liaison theory of subvarieties to sheaves, and provide a framework to study sheaves and subvarieties simultaneously.

Keywords

Cite

@article{arxiv.2004.02280,
  title  = {Biliaison of sheaves},
  author = {Mengyuan Zhang},
  journal= {arXiv preprint arXiv:2004.02280},
  year   = {2020}
}

Comments

21 pages, added a reference by Burragina that treats a special case of our theory