Geodesic
Prym-Tjurin constructions on cubic hypersurfaces
Documenta mathematica, Tome 19 (2014), pp. 867-903
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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.
DOI : 10.4171/dm/467
Classification : 14C25, 14F25
Mots-clés : Chow group, Hodge structure, incidence correspondence 
@article{10_4171_dm_467,
     author = {Mingmin Shen},
     title = {Prym-Tjurin constructions on cubic hypersurfaces},
     journal = {Documenta mathematica},
     pages = {867--903},
     year = {2014},
     volume = {19},
     doi = {10.4171/dm/467},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/467/}
}
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Mingmin Shen. Prym-Tjurin constructions on cubic hypersurfaces. Documenta mathematica, Tome 19 (2014), pp. 867-903. doi: 10.4171/dm/467

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