Geodesic
Prym-Tjurin constructions on cubic hypersurfaces
Documenta mathematica, Tome 19 (2014), pp. 867-903.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In this paper, we give a Prym-Tjurin construction for the cohomology and the Chow groups of a cubic hypersurface. On the space of lines meeting a given rational curve, there is the incidence correspondence. This correspondence induces an action on the primitive cohomology and the primitive 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. All the constructions are based on a natural relation among topological (resp. algebraic) cycles on $X$ modulo homological (resp. rational) equivalence.
Classification : 14F25, 14C25
Keywords: Hodge structure, Chow group, incidence correspondence 
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     author = {Shen, Mingmin},
     title = {Prym-Tjurin constructions on cubic hypersurfaces},
     journal = {Documenta mathematica},
     pages = {867--903},
     publisher = {mathdoc},
     volume = {19},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2014__19__a16/}
}
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Shen, Mingmin. Prym-Tjurin constructions on cubic hypersurfaces. Documenta mathematica, Tome 19 (2014), pp. 867-903. http://geodesic.mathdoc.fr/item/DOCMA_2014__19__a16/