On the existence of k-normal curves of given degree and genus in projective spaces

• Autores: N. Chiarli, Edoardo Ballico, Silvio Greco
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 55, Fasc. 3, 2004, págs. 269-278
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • We find some ranges for the $4$-tuples of integers $(d, g, n, r)$ for which there is a smooth connected non-degenerate curve of degree $d$ and genus $g$, which is $k$-normal for every $k\leq r$.

• Referencias bibliográficas
  • C. Berg, J.P.R. Christensen, and P. Ressel, Harmonic Analysis on Semigroups, Theory of Positive Definite and Related Functions, Graduate Texts...
  • T.M. Bisgaard, Characterization of perfect involution groups, Math. Scand. 65 (1989), 245–258.
  • T.M. Bisgaard, On perfect semigroups, Acta Math. Hungar. 79 (1998), 269–294.
  • T.M. Bisgaard, On perfect subsemigroups of $\mathbb{Q}\_+$, Acta Math. Hungar. 93 (2001), 77–97.
  • T.M. Bisgaard, A note on factoring of positive definite functions on semigroups, Math. Nachr. 236 (2002), 31–46.
  • T.M. Bisgaard, On the Stieltjes moment problem on semigroups, Czechoslovak Math. J. 52 (127) (2002), 155–196.
  • T.M. Bisgaard, Extensions of Herglotz' theorem, Comment. Math. Univ. St. Pauli 51 (2002), 195–215.
  • T.M. Bisgaard and P. Ressel, Unique disintegration of arbitrary positive definite functions on \*-divisible semigroups, Math. Z. 200 (1989),...
  • T.M. Bisgaard and N. Sakakibara, A reduction of the problem of characterizing perfect semigroups, Math. Scand. 91 (2002), 55–66.
  • T.M. Bisgaard and N. Sakakibara, Stieltjes perfect semigroups are perfect, Czechoslovak Math. J. to appear.
  • Y. Nakamura and N. Sakakibara, Perfectness of certain subsemigroups of a perfect semigroup, Math. Ann. 287 (1990), 213–220.
  • K. Nishio and N. Sakakibara, Perfectness of conelike \*-semigroups in $\mathbb{Q}\_+^k$, Math. Nachr. 216 (2000), 155–167.
  • N. Sakakibara, Perfectness and semiperfectness of abelian \*-semigroups without zero, Hokkaido Math. J. 24 (1995), 113–125.E. Arbarello, M....
  • G. Castelnuovo, Sui multipli di una serie lineare di gruppi di punti appartenente ad una curva algebrica, Rend. Circ. Mat. Palermo 7 (1893),...
  • L. Chiantini, N. Chiarli, and S. Greco, Halphen conditions and postulation of nodes, Advances in Geometry (to appear).
  • C. Ciliberto, On the degree and genus of smooth curves in a projective space, Adv. Math. 81 (1990), 198–248.
  • C. Ciliberto and E. Sernesi, Curves on surfaces of degree $2r-\delta$ in $\mathbb{P}^r$, Comment. Math. Helv. 64 (1989), 300–328.
  • R. Di Gennaro, Again on curves on rational normal scroll surfaces, Preprint 2003.
  • A. Dolcetti and G. Pareschi, On linearly normal space curves, Math. Z. 198 (1988), 73–82.
  • S. Giuffrida and R. Maggioni, On the Rao module of a curve lying on a smooth cubic surface in $\mathbb{P}^3$, II, Comm. Algebra 20 (1992),...
  • M. Green and R. Lazarsfeld, On the projective normality of complete linear series on an algebraic curve, Invent. Math. 83 (1985), 73–90.
  • L. Gruson and C. Peskine, Genre des courbes de l’espace projectif, II, Ann. Sci. École Norm. Sup. (4) 15 (1982), 401–418.
  • J. Harris, with the collaboration of D. Eisenbud, Curves in Projective Space, Les presses de l’Université de Montréal, Montreal, 1982.
  • R. Hartshorne, Genre des courbes algébriques dans l’espace projectif, Séminaire Bourbaki, 592, 301–313, Astérisque 92-93, 1982.
  • R. Hartshorne, On the classification of algebraic space curves, II, Algebraic Geometry, Bowdoin, 1985, 145–164, Proc. Sympos. Pure Math. 46,...
  • M. Homma, On the projective normality and defining equations of a projective curve of genus three embedded by a complete linear system, Tsukuba...
  • A.L. Knutsen, Smooth curves on projective K3 surfaces, Math. Scand. 90 (2002), 215–231.
  • A. Mattuck, Symmetric products and Jacobians, Amer. J. Math. 83 (1961), 189–206.
  • J.C. Migliore, Introduction to Liaison Theory and Deficiency Modules, Progress in Math. 165, Birkhäuser, 1998.
  • S. Mori, On degree and genera of curves on smooth quartic surfaces in $\mathbb{P}^3$, Nagoya Math. J. 96 (1984), 127–132.
  • D. Mumford, Varieties defined by quadratic equations, Corso CIME 1969, Questions on Algebraic Varieties, 30–100, Cremonese, Rome, 1970.
  • O. Pǎsǎrescu, On the existence of algebraic curves in projective $n$-space, Arch. Math. (Basel) 5 (1988), 255–265.
  • O. Pǎsǎrescu, Halphen-Castelnuovo theory for smooth curves in $\mathbb{P}^n$. I. The lacunar domain, Preprint 2000.
  • O. Pǎsǎrescu, Linearly normal curves in $\mathbb{P}^4$ and $\mathbb{P}^5$, An. Ştiinţ. Univ. Ovidius Constanţa Ser. Mat. 9 (2001), 73–79.
  • J. Rathmann, The genus of curves in $\mathbb{P}^4$ and $\mathbb{P}^5$, Math. Z. 202 (1989), 525–543.