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Some results on Green's higher Abel-Jacobi map

Claire Voisin
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Abstract

We study the higher Abel-Jacobi invariant defined recently by M. Green. We first construct a counterexample to the injectivity of Green's higher Abel-Jacobi map. On the other hand, we prove that the higher Abel-Jacobi map governs Mumford's pull-back of holomorphic forms. We deduce from this that if a surface has holomorphic 2-forms, the image of the higher Abel-Jacobi map, defined on its group of zero-cycles Albanese equivalent to 0, has infinite dimensional image.

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Claire Voisin. 1999-03-01. Some results on Green's higher Abel-Jacobi map. https://arxiv.org/abs/math/9903204

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