PROJECTORS ON THE INTERMEDIATE ALGEBRAIC JACOBIANS
By Charles Vial. 2009
73 citations recorded by the source corpus.
Let X be a complex smooth projective variety of dimension d. Under some assump- tion on the cohomology of X, we construct mutually orthogonal idempotents in CHd(X X) Q whose action on algebraically trivial cycles coincides with the Abel{Jacobi map. Such a con- struction generalizes Murre's construction of the Albanese and Picard idempotents and makes it possible to give new examples of varieties admitting a self-dual Chow{Kunneth decomposi- tion as well as new examples of varieties having a Kimura nite dimensional Chow motive. For instance, we prove that fourfolds with Chow group of zero-cycles supported on a curve (e.g. rationally connected fourfolds) have a self-dual Chow{Kunneth decomposition. We also prove that hypersurfaces of very low degree are Kimura nite dimensional.
Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/5b5d11da9e61d97634281a9f5200b73c36192269
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Citations in the corpus
- The generalized Franchetta conjecture for some hyper-Kähler varieties, II (2020, background): “In addition, cubic threefolds and fivefolds are known to be Kimura–O’Sullivan finite dimensional; see [GG12] and [Via13, Ex.”
- The Fourier Transform for Certain HyperKähler Fourfolds (2013, background): “By [49, Theorem 5], the Chow motive of X is isomorphic to a direct sum of Lefschetz motives (see [49] for the definitions) so that X has a Chow–Künneth decomposition such that the induced grading on CH(X) is concentrated in degree zero, that is, CH(X) = CHCK(X)0.”
- Algebraic cycles and fibrations (2012, background): “tisfies the Lefschetz standard conjecture. • If n= 1 and l= ⌊d−3 2 ⌋, then Xhas a Murre decomposition. • If n= 1 and l= ⌊d−2 2 ⌋, then Xis Kimura finite-dimensional. Proof. The fourth item is proved in [27]. It is also proved there that if Xis as in the third item, then X has a Chow–Ku¨nneth decomposi”