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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Focal loci of families and the genus of curves on surfaces
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by Luca Chiantini and Angelo Felice Lopez PDF
Proc. Amer. Math. Soc. 127 (1999), 3451-3459 Request permission

Abstract:

In this article we apply the classical method of focal loci of families to give a lower bound for the genus of curves lying on general surfaces. First we translate and reprove Xu’s result that any curve $C$ on a general surface in $\mathbb {P}^{3}$ of degree $d \geq 5$ has geometric genus $g > 1 + \operatorname {deg} C (d - 5) / 2$. Then we prove a similar lower bound for the curves lying on a general surface in a given component of the Noether-Lefschetz locus in $\mathbb {P}^{3}$ and on a general projectively Cohen-Macaulay surface in $\mathbb {P}^{4}$.
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Additional Information
  • Luca Chiantini
  • Affiliation: Dipartimento di Matematica, Università di Siena, Via del Capitano 15, 53100 Siena, Italy
  • MR Author ID: 194958
  • ORCID: 0000-0001-5776-1335
  • Email: chiantini@unisi.it
  • Angelo Felice Lopez
  • Affiliation: Dipartimento di Matematica, Università di Roma Tre, Largo San Leonardo Murialdo 1, 00146 Roma, Italy
  • MR Author ID: 289566
  • ORCID: 0000-0003-4923-6885
  • Email: lopez@matrm3.mat.uniroma3.it
  • Received by editor(s): February 2, 1998
  • Published electronically: July 23, 1999
  • Additional Notes: This research was partially supported by the MURST national project “Geometria Algebrica"; the authors are members of GNSAGA of CNR
  • Communicated by: Ron Donagi
  • © Copyright 1999 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 127 (1999), 3451-3459
  • MSC (1991): Primary 14J29; Secondary 32H20, 14C20
  • DOI: https://doi.org/10.1090/S0002-9939-99-05407-6
  • MathSciNet review: 1676295