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Curves of maximum genus in range A and stick-figures
Author(s):
Edoardo
Ballico;
Giorgio
Bolondi;
Philippe
Ellia;
Rosa
Maria
Mirò-Roig
Journal:
Trans. Amer. Math. Soc.
349
(1997),
4589-4608.
MSC (1991):
Primary 14H50
MathSciNet review:
1422888
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Abstract:
In this paper we show the existence of smooth connected space curves not contained in a surface of degree less than  , with genus maximal with respect to the degree, in half of the so-called range A. The main tool is a technique of deformation of stick-figures due to G. Fløystad.
References:
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- E. Ballico and Ph. Ellia, A program for space curves, Conf. Algebraic Varieties of Small Dimension, Rend. Sem. Mat. Univ. Politec. Torino, special issue (1986), 25-42. MR 89e:14031
- [E]
- Ph. Ellia, Sur le genre maximal des courbes gauches de degré
 non sur une surface de degré  , J. Reine Angew. Math. 413 (1991), 78-87. MR 92a:14029 - [ES]
- Ph. Ellia and R. Strano, Sections planes et majoration du genre des courbes gauches, Complex Projective Geometry, London Math. Soc. Lecture Note Ser., vol. 179, Cambridge Univ. Press, Cambridge and New York, 1992, pp. 157-174. MR 94b:14028
- [F]
- G. Fløystad, Construction of space curves with good properties, Math. Ann. 289 (1991), 33-54. MR 92h:14021
- [GP1]
- L. Gruson and Chr. Peskine, Genre des courbes de l'espace projectif, Algebraic Geometry (Tromsø, 1977), Lecture Notes in Math., vol. 687, Springer-Verlag, New York and Berlin, 1978, pp. 31-59. MR 81e:14019
- [GP2]
- -, Postulation des courbes gauches, Algebraic Geometry (Ravello, 1982), Lecture Notes in Math., vol. 997, Springer-Verlag, New York and Berlin, 1983, pp. 218-227. MR 85f:14029
- [H]
- G. H. Halphen, Mémoire sur la classification des courbes gauches algébriques, Ouvres Completes, t. III, pp. 261-455.
- [Ha1]
- R. Hartshorne, On the classification of algebraic spaces curves II, Proc. Sympos. Pure Math., vol. 46, Amer. Math. Soc., Providence, RI, 1987, pp. 145-164. MR 89g:14025
- [Ha2]
- -, Stable reflexive sheaves III, Math. Ann. 279 (1988), 517-534. MR 89h:14011
- [HH1]
- R. Hartshorne and A. Hirschowitz, Smoothing algebraic space curves, Algebraic Geometry (Sitges, 1983), Lecture Notes in Math., vol. 1124, Springer-Verlag, New York and Berlin, 1985, pp. 98-131. MR 87h:14023
- [HH2]
- -, Nouvelles courbes de bon genre dans l'espace projectif, Math. Ann. 280 (1988), 353-367. MR 89d:14043
- [S1]
- R. Strano, Plane sections of curves of
 and a conjecture of Hartshorne and Hirschowitz, Rend. Sem. Mat. Univ. Politec. Torino 48 (1990), 511-527. MR 94e:14041 - [S2]
- -, On the genus of a maximal rank curve in
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Additional Information:
Edoardo
Ballico
Affiliation:
Dipartimento di Matematica, Università di Trento, I-38050 Povo (Trento), Italy
Email:
ballico@science.unitn.it
Giorgio
Bolondi
Affiliation:
Istituto di Matematica e Fisica, Università di Sassari, Via Vienna 2, I-07100 Sassari, Italy
Email:
bolondi@science.unitn.it
Philippe
Ellia
Affiliation:
Dipartimento di Matematica, Università di Ferrara, Via Machiavelli 35, I-44100 Ferrara, Italy
Email:
phe@dns.unife.it
Rosa
Maria
Mirò-Roig
Affiliation:
Departimento Algebra y Geometrìa, Facultad de Matemàticas, Universidad de Barcelona, 08007 Barcelona, Spain
Email:
miro@cerber.ub.es
DOI:
10.1090/S0002-9947-97-01917-X
PII:
S 0002-9947(97)01917-X
Keywords:
Stick-figures,
maximum genus
Received by editor(s):
March 11, 1996
Copyright of article:
Copyright
1997,
American Mathematical Society
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