Morphisms on an Algebraic Curve and Divisor Classes in the Self Product

Lucio Guerra

Bollettino dell'Unione Matematica Italiana (2007)

  • Volume: 10-B, Issue: 3, page 715-725
  • ISSN: 0392-4033

Abstract

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Morphisms on a curve may be seen as homology classes in the self product. We describe these classes as belonging to an intersection: the locus of integral points of an algebraic set in the complex homology group, and the locus of effective divisor classes. We write down explicit equations for the algebraic set, and in the case of genus three we compute a few explicit solutions over the rationals.

How to cite

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Guerra, Lucio. "Morphisms on an Algebraic Curve and Divisor Classes in the Self Product." Bollettino dell'Unione Matematica Italiana 10-B.3 (2007): 715-725. <http://eudml.org/doc/290425>.

@article{Guerra2007,
abstract = {Morphisms on a curve may be seen as homology classes in the self product. We describe these classes as belonging to an intersection: the locus of integral points of an algebraic set in the complex homology group, and the locus of effective divisor classes. We write down explicit equations for the algebraic set, and in the case of genus three we compute a few explicit solutions over the rationals.},
author = {Guerra, Lucio},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {715-725},
publisher = {Unione Matematica Italiana},
title = {Morphisms on an Algebraic Curve and Divisor Classes in the Self Product},
url = {http://eudml.org/doc/290425},
volume = {10-B},
year = {2007},
}

TY - JOUR
AU - Guerra, Lucio
TI - Morphisms on an Algebraic Curve and Divisor Classes in the Self Product
JO - Bollettino dell'Unione Matematica Italiana
DA - 2007/10//
PB - Unione Matematica Italiana
VL - 10-B
IS - 3
SP - 715
EP - 725
AB - Morphisms on a curve may be seen as homology classes in the self product. We describe these classes as belonging to an intersection: the locus of integral points of an algebraic set in the complex homology group, and the locus of effective divisor classes. We write down explicit equations for the algebraic set, and in the case of genus three we compute a few explicit solutions over the rationals.
LA - eng
UR - http://eudml.org/doc/290425
ER -

References

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  1. KANI, E., Bounds on the number of non-rational subfields of a function field, Invent. Math., 85 (1986), 185-198. Zbl0615.12017MR842053DOI10.1007/BF01388797
  2. MARTENS, H., Mappings of closed Riemann surfaces, Theta functions-Bowdoin 1987, Part 1, 531-539, Proc. Sympos. Pure Math., 49, Part 1, Amer. Math. Soc., 1989. MR1013150
  3. NARANJO, J. C. - PIROLA, G. P., Bounds of the number of rational maps between varieties of general type, ArXiv:math.AG/0511463. MR2369893DOI10.1353/ajm.2007.0040
  4. SAMUEL, P., Old and new results on algebraic curves, Tata Inst. Fund. Res.Bombay, 1966. Zbl0165.24102MR222088
  5. TANABE, M., Bounds on the number of holomorphic maps of compact Riemann surfaces, Proc. Amer. Math. Soc., 133 (2005), 3057-3064. Zbl1072.30031MR2159785DOI10.1090/S0002-9939-05-07882-2
  6. WEIL, A., Sur les courbes algébriques et les variétés qui s'en deduisent, Hermann, Paris, 1948. Zbl0036.16001MR27151

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