Ballico, Edoardo and Keem, Changho and Kim, Seonja:
Normal generation of line bundles on a general $k$-gonal algebraic curve
Bollettino dell'Unione Matematica Italiana Serie 8 6-B (2003), fasc. n.3, p. 557-562, Unione Matematica Italiana (English)
pdf (233 Kb), djvu (89 Kb). | MR2014818 | Zbl 1178.14030
Sunto
Sia $X$ una curva $k$-gonale generale di genere $g$ ed $L \in \text{Pic}^{d}(X)$ con $d:= \text{deg} L > (3g-1)/2$, $h^{1}(X, L)\neq 0$ ed $L$ molto ampio. In questo lavoro dimostriamo che $L$ è normalmente generato se il luogo base di $KL^{-1}$ ha grado al massimo $c(k-2)/2$ con $c:= d-(3g-1)/2$.
Referenze Bibliografiche
[ACGH]
E. ARBARELLO-
M. CORNALBA-
P. A. GRIFFITHS-
J. HARRIS,
Geometry of Algebraic Curves I,
Springer Verlag,
1985. |
MR 770932 |
Zbl 0559.14017[B]
E. BALLICO,
On Projectively Normal Embeddings of General $k$-gonal Curves,
Ann. Univ. Ferrara, Sez. VII, Sc. Mat.,
XLV (
1999), 123-125. |
MR 1802479 |
Zbl 1042.14502[CKM]
M. COPPENS-
C. KEEM-
G. MARTENS,
Primitive linear series on curves,
Manuscripta Math.,
77 (
1992), 237-264. |
MR 1188583 |
Zbl 0786.14016[GL]
M. GREEN-
R. LAZARSFELD,
On the projective normality of complete linear series on an algebraic curve,
Invent. Math.,
83 (
1986), 73-90. |
MR 813583 |
Zbl 0594.14010[K]
S. KIM,
On the Clifford sequence of a general $k$-gonal curve,
Indag. Math., N.S.8 (
1997), 209-216. |
MR 1621995 |
Zbl 0890.14014[LM]
H. LANGE-
G. MARTENS,
Normal generation and presentation of line bundles of low degree on curves,
J. reine angew. Math.,
356 (
1985), 1-18. |
MR 779373 |
Zbl 0561.14009[Mu]
D. MUMFORD,
Varieties defined by quadric equations, Corso C.I.M.E. 1969, in
Questions on Algebraic Varieties,
Cremonese, Rome,
83 (
1970), 30-100. |
MR 282975 |
Zbl 0198.25801