NORMAL GENERATION OF NONSPECIAL LINE BUNDLES ON ALGEBRAIC CURVES

Title & Authors
NORMAL GENERATION OF NONSPECIAL LINE BUNDLES ON ALGEBRAIC CURVES
Kim, Seon-Ja; Kim, Young-Rock;

Abstract
In this paper, we classify (C, $\small{\cal{L}}$) such that a smooth curve C of genus g has a nonspecial very ample line bundle $\small{\cal{L}}$ of deg $\small{\cal{L}}$
Keywords
algebraic curve;linear series;line bundle;projectively normal;normal generation;
Language
English
Cited by
References
1.
E. Arbarello, M. Cornalba, P. A. Griffiths, and J. Harris, Geometry of Algebraic Curves. Vol. I, Springer-Verlag, New York, 1985.

2.
E. Ballico, On the Clifford index of algebraic curves, Proc. Amer. Math. Soc. 97 (1986), no. 2, 217-218.

3.
G. Castelnuovo, Sui multipli di una serie lineare di gruppi di punti appartenente ad una curva algebrica, Rend. Circ. Mat. Palermo 7 (1893), 89-110.

4.
M. Coppens and G. Martens, Secant spaces and Clifford's theorem, Compositio Math. 78 (1991), no. 2, 193-212.

5.
M. Green and R. Lazarsfeld, On the projective normality of complete linear series on an algebraic curve, Invent. Math. 83 (1985), no. 1, 73-90.

6.
R. Hartshorne, Algebraic Geometry, Graduate Text in Math, 52, Berlin-Heidelberg-New York 1977.

7.
C. Keem and S. Kim, On the Clifford index of a general (e+2)-gonal curve, Manuscripta Math. 63 (1989), no. 1, 83-88.

8.
S. Kim and Y. Kim, Projectively normal embedding of a k-gonal curve, Comm. Algebra 32 (2004), no. 1, 187-201.

9.
S. Kim and Y. Kim, Normal generation of line bundles on algebraic curves, J. Pure Appl. Algebra 192 (2004), no. 1-3, 173-186.

10.
T. Kato, C. Keem, and A. Ohbuchi, Normal generation of line bundles of high degrees on smooth algebraic curves, Abh. Math. Sem. Univ. Hamburg 69 (1999), 319-333.

11.
H. Lange and G. Martens, Normal generation and presentation of line bundles of low degree on curves, J. Reine Angew. Math. 356 (1985), 1-18.

12.
G. Martens and F. O. Schreyer, Line bundles and syzygies of trigonal curves, Abh. Math. Sem. Univ. Hamburg 56 (1986), 169-189.

13.
D. Mumford, Varieties defined by quadric equations, Questions on Algebraic Varieties (C.I.M.E., III Ciclo, Varenna, 1969) pp. 29-100 Edizioni Cremonese, Rome, 1970.