English

The reduction number and degree bound of projective subschemes

Algebraic Geometry 2019-08-06 v2 Commutative Algebra

Abstract

In this paper, we prove the degree upper bound of projective subschemes in terms of the reduction number and show that the maximal cases are only arithmetically Cohen-Macaulay subschemes with linear resolution. Furthermore, it can be shown that there are only two types of reduced, irreducible projective varieties with almost maximal degree. We also give explicit Betti tables for almost maximal cases. Interesting examples are provided to understand our main results.

Keywords

Cite

@article{arxiv.1811.08386,
  title  = {The reduction number and degree bound of projective subschemes},
  author = {Doan Trung Cuong and Sijong Kwak},
  journal= {arXiv preprint arXiv:1811.08386},
  year   = {2019}
}