ALGEBRAIC CYCLES ON QUADRIC SECTIONS OF CUBICS IN P-4 UNDER THE ACTION OF SYMPLECTOMORPHISMS

作者：Guletskii V^*; Tikhomirov A^*

来源：Proceedings of the Edinburgh Mathematical Society, 2016, 59(2): 377-392.

DOI：10.1017/S0013091515000176

• algebraic cycles
• K3-surfaces
• symplectomorphism
• mixed Hodge structures
• cubic threefolds
• intermediate Jacobian

Let tau be the involution changing the sign of two coordinates in P-4. We prove that tau induces the identity action on the second Chow group of the intersection of a tau-invariant cubic with a tau-invariant quadric hypersurface in P-4. Let l(tau) and Pi(tau) be the one-and two-dimensional components of the fixed locus of the involution tau. We describe the generalized Prymian associated with the projection of a tau-invariant cubic l subset of P-4 from l(tau) onto Pi(tau) in terms of the Prymians P-2 and P-3 associated with the double covers of two irreducible components, of degree 2 and 3, respectively, of the reducible discriminant curve. This gives a precise description of the induced action of the involution t on the continuous part of the Chow group CH2(l). The action on the subgroup corresponding to P-3 is the identity, and the action on the subgroup corresponding to P-2 is the multiplication by -1.

• 出版日期2016-5