The reduction number and degree bound of projective subschemes

2018/11/20 by Cuong, Doan Trung, Kwak, Sijong
#13D02 #14N05 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1811.08386

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.

Related

• Minimal free resolutions of projective subschemes of small degree
• Degrees of generators of ideals defining subschemes of projective space
• Characterization of projective varieties beyond varieties of minimal degree and del Pezzo varieties
• Arithmetic properties of projective varieties of almost minimal degree
• Good reduction and canonical heights of subvarieties