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Linear normality of general linear sections and some graded Betti numbers of 3-regular projective schemes

Title
Linear normality of general linear sections and some graded Betti numbers of 3-regular projective schemes
Authors
Ahn, JeamanHan, Kangjin
DGIST Authors
Han, Kangjin
Issue Date
2015-10-15
Citation
Journal of Algebra, 440, 642-667
Type
Article
Article Type
Article
Keywords
3-Regular SchemeGeneric Initial IdealsGraded Betti NumbersLinear Normality
ISSN
0021-8693
Abstract
In this paper we study graded Betti numbers of any nondegenerate 3-regular algebraic set X in a projective space Pn. More concretely, via Generic initial ideals (Gins) method we mainly consider 'tailing' Betti numbers, whose homological index is at least codim(X,Pn). For this purpose, we first introduce a key definition 'ND(1) property', which provides a suitable ground where one can generalize the concepts such as 'being nondegenerate' or 'of minimal degree' from the case of varieties to the case of more general closed subschemes and give a clear interpretation on the tailing Betti numbers. Next, we recall basic notions and facts on Gins theory and we analyze the generation structure of the reverse lexicographic (rlex) Gins of 3-regular ND(1) subschemes. As a result, we present exact formulae for these tailing Betti numbers, which connect them with linear normality of general linear sections of X∩. Λ with a linear subspace Λ of dimension at least codim(X,Pn). Finally, we consider some applications and related examples. © 2015 Elsevier Inc..
URI
http://hdl.handle.net/20.500.11750/5163
DOI
10.1016/j.jalgebra.2015.06.030
Publisher
Academic Press Inc.
Files:
There are no files associated with this item.
Collection:
School of Undergraduate Studies1. Journal Articles


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