Higher syzygies of hyperelliptic curves
- Authors
- Park, Euisung
- Issue Date
- 2월-2010
- Publisher
- ELSEVIER
- Keywords
- Hyperelliptic Curve; Minimal free resolution
- Citation
- JOURNAL OF PURE AND APPLIED ALGEBRA, v.214, no.2, pp.101 - 111
- Indexed
- SCIE
SCOPUS
- Journal Title
- JOURNAL OF PURE AND APPLIED ALGEBRA
- Volume
- 214
- Number
- 2
- Start Page
- 101
- End Page
- 111
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/117115
- DOI
- 10.1016/j.jpaa.2009.04.006
- ISSN
- 0022-4049
- Abstract
- Let X be a hyperelliptic curve of arithmetic genus g and let f : X -> P-1 be the hyperelliptic involution map of X. In this paper we study higher syzygies of linearly normal embeddings of X of degree d <= 2g. Note that the minimal free resolution of X of degree >= 2g + 1 is already completely known. Let A = f*O-P1(1), and let L be a very ample line bundle on X of degree d <= 2g. For m = max {t is an element of Z} H-0(X, L circle times A(-t)) not equal 0}, we call the pair (m, d-2m) the factorization type of L. Our main result is that the Hartshorne-Rao module and the graded Betti numbers of the linearly normal curve embedded by vertical bar L vertical bar are precisely determined by the factorization type of L. (C) 2009 Elsevier B.V. All rights reserved.
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