In a previous paper we described the collection of homological equivalence relations on a curve of genus as the set of integral solutions of certain algebraic equations. In the present paper we improve one argument of the previous paper, and we study the equations more closely for a curve of genus 2.
@article{BUMI_2010_9_3_3_505_0,
author = {Lucio Guerra},
title = {Remarks About Morphisms on an Algebraic Curve},
journal = {Bollettino dell'Unione Matematica Italiana},
volume = {3},
year = {2010},
pages = {505-519},
zbl = {1215.14038},
mrnumber = {2742779},
language = {en},
url = {http://dml.mathdoc.fr/item/BUMI_2010_9_3_3_505_0}
}
Guerra, Lucio. Remarks About Morphisms on an Algebraic Curve. Bollettino dell'Unione Matematica Italiana, Tome 3 (2010) pp. 505-519. http://gdmltest.u-ga.fr/item/BUMI_2010_9_3_3_505_0/
[1] - , Complex Abelian Varieties, second edition. Springer-Verlag, Berlin, 2004. | MR 2062673 | Zbl 1056.14063
[2] , Introduction to the Theory of Numbers. Dover Publications, New York, 1957. | Zbl 0084.26901
[3] , Morphisms on an algebraic curve and divisor classes in the self product. Boll. Unione Mat. Ital. Sez. B (8) 10, no. 3 (2007), 715-725. | MR 2351541 | Zbl 1139.14030
[4] - , Existence of curves of genus two on a product of two elliptic curves. J. Math. Soc. Japan, 17 (1965), 1-16. | MR 201434 | Zbl 0132.41701
[5] , Bounds on the number of nonrational subfields of a function field. Invent. Math., 85 , no. 1 (1986), 185-198. | MR 842053 | Zbl 0615.12017
[6] , Curves of genus 2 with split Jacobian. Trans. Amer. Math. Soc., 307 , no. 1 (1988), 41-49. | MR 936803 | Zbl 0692.14022
[7] - , Geometric uniformization in genus 2. Ann. Acad. Sci. Fenn. Ser. A I Math., 20, no. 2 (1995), 401-418. | MR 1346823 | Zbl 0856.30031