# 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

## Access Full Article

top## Abstract

top## How to cite

topBallico, 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

top- ARBARELLO, E.- CORNALBA, M.- GRIFFITHS, P. A.- HARRIS, J., Geometry of Algebraic Curves I, Springer Verlag, 1985. Zbl0559.14017MR770932
- BALLICO, E., On Projectively Normal Embeddings of General $k$-gonal Curves, Ann. Univ. Ferrara, Sez. VII, Sc. Mat., XLV (1999), 123-125. Zbl1042.14502MR1802479
- COPPENS, M.- KEEM, C.- MARTENS, G., Primitive linear series on curves, Manuscripta Math., 77 (1992), 237-264. Zbl0786.14016MR1188583
- GREEN, M.- LAZARSFELD, R., On the projective normality of complete linear series on an algebraic curve, Invent. Math., 83 (1986), 73-90. Zbl0594.14010MR813583
- KIM, S., On the Clifford sequence of a general $k$-gonal curve, Indag. Math., N.S.8 (1997), 209-216. Zbl0890.14014MR1621995
- 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
- 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

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.