P. A. Griffiths has shown [Ann. of Math. (2) 90 (1969), 460–495; ibid. (2) 90 (1969), 496–541;] that it is not true that algebraic and homological equivalence with rational coefficients always coincide, but it is an open question...whether they coincide on abelian varieties. We prove that Poincar´e’s formulas hold for algebraic equivalence when J is the Jacobian variety of a hyperelliptic curve.”
Poincaré's formulas and hyperelliptic curves.Atti Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur.
COLLINO, Alberto
1975-01-01
Abstract
P. A. Griffiths has shown [Ann. of Math. (2) 90 (1969), 460–495; ibid. (2) 90 (1969), 496–541;] that it is not true that algebraic and homological equivalence with rational coefficients always coincide, but it is an open question...whether they coincide on abelian varieties. We prove that Poincar´e’s formulas hold for algebraic equivalence when J is the Jacobian variety of a hyperelliptic curve.”
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