| 研究実績の概要 |
Ths year we worked on an application of the complex of admissible chains we constructed before. Concretely, we gave a new way of describing relative cohomology groups of smooth quasi-projective varieties, and duality pairing of cohomology groups in terms of period integrals. Main ingredients in the proof is Cauchy-Stokes formula generalizing classical Cauchy integral formula to the situation of semi-algebraic chains. As an application, we gave a new description of the Abel-Jacobi map for higher Chow cycles which is a natural generalization of the Abel-Jacobi map for ordinary algebraic cycles defined by Griffiths. An example is the Hodge realization of Polylog cycles defined by Bloch.
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