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The Hodge cohomology and cubic equivalences

Published online by Cambridge University Press:  22 January 2016

Hiroshi Saito
Hiroshi Saito*
Affiliation:
Department of Mathematics, Nagoya University, Nagoya, 464, Japan
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In 1969, Mumford [8] proved that, for a complete non-singular algebraic surface F over the complex number field C, the dimension of the Chow group of zero-cycles on F is infinite if the geometric genus of F is positive. To this end, he defined a regular 2-form ηf on a non-singular variety S for a regular 2-form η on F and for a morphism f: S → SnF, where SnF is the 72-th symmetric product of F, and he showed that ηf vanishes if all 0-cycles f(s), s ∈ S, are rationally equivalent. Roitman [9] later generalized this to a higher dimensional smooth projective variety V.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 94 , June 1984 , pp. 1 - 41
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1984

References

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