Normal generation of line bundles on a general k -gonal algebraic curve

Edoardo Ballico; Changho Keem; Seonja Kim

Bollettino dell'Unione Matematica Italiana (2003)

  • Volume: 6-B, Issue: 3, page 557-562
  • ISSN: 0392-4033

Abstract

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We prove that a very ample special line bundle L of degree d > 3 g - 1 / 2 on a general k -gonal curve is normally generated if the degree of the base locus of its dual bundle K L - 1 does not exceed c k - 2 / 2 , where c := d - 3 g - 1 / 2 .

How to cite

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Ballico, Edoardo, Keem, Changho, and Kim, Seonja. "Normal generation of line bundles on a general $k$-gonal algebraic curve." Bollettino dell'Unione Matematica Italiana 6-B.3 (2003): 557-562. <http://eudml.org/doc/195045>.

@article{Ballico2003,
abstract = {We prove that a very ample special line bundle $L$ of degree $d>(3g-1)/2$ on a general $k$-gonal curve is normally generated if the degree of the base locus of its dual bundle $KL^\{-1\}$ does not exceed $c(k-2)/2$, where $c:= d-(3g-1)/2$.},
author = {Ballico, Edoardo, Keem, Changho, Kim, Seonja},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {557-562},
publisher = {Unione Matematica Italiana},
title = {Normal generation of line bundles on a general $k$-gonal algebraic curve},
url = {http://eudml.org/doc/195045},
volume = {6-B},
year = {2003},
}

TY - JOUR
AU - Ballico, Edoardo
AU - Keem, Changho
AU - Kim, Seonja
TI - Normal generation of line bundles on a general $k$-gonal algebraic curve
JO - Bollettino dell'Unione Matematica Italiana
DA - 2003/10//
PB - Unione Matematica Italiana
VL - 6-B
IS - 3
SP - 557
EP - 562
AB - We prove that a very ample special line bundle $L$ of degree $d>(3g-1)/2$ on a general $k$-gonal curve is normally generated if the degree of the base locus of its dual bundle $KL^{-1}$ does not exceed $c(k-2)/2$, where $c:= d-(3g-1)/2$.
LA - eng
UR - http://eudml.org/doc/195045
ER -

References

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  1. ARBARELLO, E.- CORNALBA, M.- GRIFFITHS, P. A.- HARRIS, J., Geometry of Algebraic Curves I, Springer Verlag, 1985. Zbl0559.14017MR770932
  2. BALLICO, E., On Projectively Normal Embeddings of General k -gonal Curves, Ann. Univ. Ferrara, Sez. VII, Sc. Mat., XLV (1999), 123-125. Zbl1042.14502MR1802479
  3. COPPENS, M.- KEEM, C.- MARTENS, G., Primitive linear series on curves, Manuscripta Math., 77 (1992), 237-264. Zbl0786.14016MR1188583
  4. GREEN, M.- LAZARSFELD, R., On the projective normality of complete linear series on an algebraic curve, Invent. Math., 83 (1986), 73-90. Zbl0594.14010MR813583
  5. KIM, S., On the Clifford sequence of a general k -gonal curve, Indag. Math., N.S.8 (1997), 209-216. Zbl0890.14014MR1621995
  6. LANGE, H.- MARTENS, G., Normal generation and presentation of line bundles of low degree on curves, J. reine angew. Math., 356 (1985), 1-18. Zbl0561.14009MR779373
  7. MUMFORD, D., Varieties defined by quadric equations, Corso C.I.M.E. 1969, in Questions on Algebraic Varieties, Cremonese, Rome, 83 (1970), 30-100. Zbl0198.25801MR282975

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