Curves of maximum genus in range A and stick-figures
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- by Edoardo Ballico, Giorgio Bolondi, Philippe Ellia and Rosa Maria Mirò-Roig PDF
- Trans. Amer. Math. Soc. 349 (1997), 4589-4608 Request permission
Abstract:
In this paper we show the existence of smooth connected space curves not contained in a surface of degree less than $m$, 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
- E. Ballico and Ph. Ellia, A program for space curves, Rend. Sem. Mat. Univ. Politec. Torino Special Issue (1986), 25–42 (1987). Conference on algebraic varieties of small dimension (Turin, 1985). MR 908909
- Philippe Ellia, Sur le genre maximal des courbes gauches de degré $d$ non sur une surface de degré $s-1$, J. Reine Angew. Math. 413 (1991), 78–87 (French). MR 1089797, DOI 10.1515/crll.1991.413.78
- Philippe Ellia and Rosario Strano, Sections planes et majoration du genre des courbes gauches, Complex projective geometry (Trieste, 1989/Bergen, 1989) London Math. Soc. Lecture Note Ser., vol. 179, Cambridge Univ. Press, Cambridge, 1992, pp. 157–174 (French). MR 1201381, DOI 10.1017/CBO9780511662652.012
- Gunnar Fløystad, Construction of space curves with good properties, Math. Ann. 289 (1991), no. 1, 33–54. MR 1087234, DOI 10.1007/BF01446556
- Laurent Gruson and Christian Peskine, Genre des courbes de l’espace projectif, Algebraic geometry (Proc. Sympos., Univ. Tromsø, Tromsø, 1977) Lecture Notes in Math., vol. 687, Springer, Berlin, 1978, pp. 31–59 (French). MR 527229
- Laurent Gruson and Christian Peskine, Postulation des courbes gauches, Algebraic geometry—open problems (Ravello, 1982) Lecture Notes in Math., vol. 997, Springer, Berlin, 1983, pp. 218–227 (French). MR 714751, DOI 10.1007/BFb0061646
- G. H. Halphen, Mémoire sur la classification des courbes gauches algébriques, Ouvres Completes, t. III, pp. 261–455.
- Robin Hartshorne, On the classification of algebraic space curves. II, Algebraic geometry, Bowdoin, 1985 (Brunswick, Maine, 1985) Proc. Sympos. Pure Math., vol. 46, Amer. Math. Soc., Providence, RI, 1987, pp. 145–164. MR 927954, DOI 10.2307/2214923
- Robin Hartshorne, Stable reflexive sheaves. III, Math. Ann. 279 (1988), no. 3, 517–534. MR 922432, DOI 10.1007/BF01456285
- R. Hartshorne and A. Hirschowitz, Smoothing algebraic space curves, Algebraic geometry, Sitges (Barcelona), 1983, Lecture Notes in Math., vol. 1124, Springer, Berlin, 1985, pp. 98–131. MR 805332, DOI 10.1007/BFb0074998
- R. Hartshorne and A. Hirschowitz, Nouvelles courbes de bon genre dans l’espace projectif, Math. Ann. 280 (1988), no. 3, 353–367 (French). MR 936316, DOI 10.1007/BF01456330
- R. Strano, Plane sections of curves of $\mathbf P^3$ and a conjecture of Hartshorne and Hirschowitz, Rend. Sem. Mat. Univ. Politec. Torino 48 (1990), no. 4, 511–527 (1993). Commutative algebra and algebraic geometry, I (Italian) (Turin, 1990). MR 1217775
- Rosario Strano, On the genus of a maximal rank curve in $\textbf {P}^3$, J. Algebraic Geom. 3 (1994), no. 3, 435–447. MR 1269715
Additional Information
- Edoardo Ballico
- Affiliation: Dipartimento di Matematica, Università di Trento, I-38050 Povo (Trento), Italy
- MR Author ID: 30125
- 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
- MR Author ID: 125375
- ORCID: 0000-0003-1375-6547
- Email: miro@cerber.ub.es
- Received by editor(s): March 11, 1996
- © Copyright 1997 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 349 (1997), 4589-4608
- MSC (1991): Primary 14H50
- DOI: https://doi.org/10.1090/S0002-9947-97-01917-X
- MathSciNet review: 1422888