✍ Scribed by James D. Lewis
No coin nor oath required. For personal study only.
Let Y be a smooth projective algebraic surface over C , and T ( Y ) the kernel of the Albanese map c f f O ( Y ) d . g o -+ Alb(Y). It was first proven by D. MUMFORD that if the genus Pg(Y) > 0, then T ( Y ) is 'infinite dimensional'. One would like to have a better idea about the structure of T(Y). For example, if Y is dominated by a product of curves El x Ez, such as an abelian or a Kummer surface, then one can easily construct an abelian variety B and a surjective 'regular' homomorphism B@Z2 4 T ( Y ) . A similar story holds for the case where Y is the Fano surface of lines on a smooth cubic hypersurface in P4. This implies a sort of boundedness result for
It is natural to ask if this is the case for any smooth projective algebraic surface Y ? Partial results have been attained in this direction by the author [Illinois. J. Math. 35 (2), 19911. In this paper, we show that the answer to this question is in general no. Furthermore, we generalize this question to the case of the Chow group of k-cycles on any projective algebraic manifold X, and arrive at, from a conjectural standpoint, necessary and sufficient cohomological conditions on X for which the question can be answered affirmatively.
z E CHk(Y x X ) , the map given by t E Y H 9 o z*((t) -( p ) ) E A is a morphism of varieties.
📜 SIMILAR VOLUMES
## Abstract In the three‐dimensional texture analysis generalized spherical functions of certain symmetries are being used in order to develop the texture function into a series. The lower order members of this series are closely related to the symmetry of physical properties of textured materials