Prym-Tjurin Constructions on Cubic Hypersurfaces

Details Prym-Tjurin Constructions on Cubic Hypersurfaces Prym-Tjurin Constructions on Cubic Hypersurfaces

2011-11-28

arxiv.org/abs/1111.6327v2

Mathematics

Algebraic Geometry

18 pages. Some errors corrected; Main theorem modified; Introduction rewritten

Scientific paper

In this paper, we give a Prym-Tjurin construction for the cohomology and Chow groups for a cubic hypersurface. On the space of lines meeting a given rational curve, there is the incidence correspondence. This correspondence induces an action on both primitive cohomology and Chow groups. We first show that this action satisfies a quadratic equation. Then the Abel-Jacobi mapping induces an isomorphism between the primitive cohomology of the cubic hypersurface and the Prym-Tjurin part of the above action. This also holds for Chow groups with rational coefficients.

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