Algebraic cycles on quadric sections of cubics in P^4 under the action of symplectomorphisms

Details Algebraic cycles on quadric sections of cubics in P^4 under the action of symplectomorphisms Algebraic cycles on quadric sections of cubics in P^4 under the action of symplectomorphisms

2011-09-26

arxiv.org/abs/1109.5725v2

Mathematics

Algebraic Geometry

38 pages

Scientific paper

The Bloch-Beilinson conjecture implies that the action of a symplectomorphism on the second Chow group of a K3-surface must be the identity. Generalizing the method developed by C.Voisin we non-conjecturally prove the identity action of the Nikulin involution on the second Chow group for intersections of cubics and quadrics in P^4. Then we give explicit geometrical description of the invariant and anti-invariant components of the Prym variety associated to a smooth cubic 3-fold invariant under the above involution, and use it to show that the anti-invariant component vanishes when passing to 0-cycles on the generic fibre of an intersection with a pencil of invariant quadrics in P^4.

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