Some remarks on Set-theoretic Intersection Curves in P 3

Roberto Paoletti

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1996)

  • Volume: 7, Issue: 1, page 41-46
  • ISSN: 1120-6330

Abstract

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Motivated by the notion of Seshadri-ampleness introduced in [11], we conjecture that the genus and the degree of a smooth set-theoretic intersection C ⊂ P 3 should satisfy a certain inequality. The conjecture is verified for various classes of set-theoretic complete intersections.

How to cite

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Paoletti, Roberto. "Some remarks on Set-theoretic Intersection Curves in \( \mathbb{P}^{3} \)." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 7.1 (1996): 41-46. <http://eudml.org/doc/244192>.

@article{Paoletti1996,
abstract = {Motivated by the notion of Seshadri-ampleness introduced in [11], we conjecture that the genus and the degree of a smooth set-theoretic intersection \( C \subset \mathbb\{P\}^\{3\} \) should satisfy a certain inequality. The conjecture is verified for various classes of set-theoretic complete intersections.},
author = {Paoletti, Roberto},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Set-theoretic intersection; Seshadri-ampleness; Genus; Degree; projective space curve; degree; genus; smooth connected set-theoretic complete intersection},
language = {eng},
month = {5},
number = {1},
pages = {41-46},
publisher = {Accademia Nazionale dei Lincei},
title = {Some remarks on Set-theoretic Intersection Curves in \( \mathbb\{P\}^\{3\} \)},
url = {http://eudml.org/doc/244192},
volume = {7},
year = {1996},
}

TY - JOUR
AU - Paoletti, Roberto
TI - Some remarks on Set-theoretic Intersection Curves in \( \mathbb{P}^{3} \)
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1996/5//
PB - Accademia Nazionale dei Lincei
VL - 7
IS - 1
SP - 41
EP - 46
AB - Motivated by the notion of Seshadri-ampleness introduced in [11], we conjecture that the genus and the degree of a smooth set-theoretic intersection \( C \subset \mathbb{P}^{3} \) should satisfy a certain inequality. The conjecture is verified for various classes of set-theoretic complete intersections.
LA - eng
KW - Set-theoretic intersection; Seshadri-ampleness; Genus; Degree; projective space curve; degree; genus; smooth connected set-theoretic complete intersection
UR - http://eudml.org/doc/244192
ER -

References

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  3. CILIBERTO, C., Canonical Surfaces with p g = p a = 4 and K 2 = 5 , … , 10 . Duke Math. J., 48, 1981, 121-157. Zbl0468.14011MR610180
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  8. JAFFE, D., Smooth curves on a cone which pass through its vertex. Manuscripta Mathematica, 73, 1991, 187-205. Zbl0779.14019MR1128687DOI10.1007/BF02567638
  9. LE BARZ, P., Formules pour les trisécantes des surfaces algébriques. L'Enseign. Math., 33, 1987, 1-66. Zbl0629.14037MR896383
  10. OKONEK, C. - SCHNEIDER, M. - SPINDLER, H., Vector bundles on complex projective spaces. Progr. in Math., vol. 56, Birkhäuser, Boston1985. Zbl0438.32016MR561910
  11. PAOLETTI, R., Seshadri positive curves in a smooth projective 3-fold. Rend. Mat. Acc. Lincei, s. 9, v. 6, 1995, 259-274. Zbl0874.14018MR1382710
  12. PESKINE, C. - SZPIRO, L., Liaison des variétés algébriques. Inv. Math., 26, 1974, 271-302. Zbl0298.14022MR364271
  13. RAO, P., On self-linked curves. Duke Math. J., 49, 1982, 251-273. Zbl0499.14014MR659940

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