Homological equivalence, modulo algebraic equivalence, is not finitely generated
Homological equivalence, modulo algebraic equivalence, is not finitely generated
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DOI：
10.1007/bf02953771
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发表时间：
1983-12
期刊：
影响因子：
--
通讯作者：
H. Clemens
中科院分区：
文献类型：
--
作者：
H. Clemens
We should include a word of warning about the use of the term.(< generic 5?. It should be taken to mean that there is a countable union of proper closed subvarieties of the set of all quintic threefolds such that the results hold for all V in the complement of that countable union.There are three steps in the proof of (0.2). First we construct an infinite sequence of rational curves on a generic quintic V such that each curve has negative normal bundle. Then we deform to quintics with nodes in such a way that exactly one of the rational curves of the sequence comes to pass through a node. Finally we use the asymptotic properties of the Abel-Jacobi mapping developed in [i] and [2] to see that the image of the rational curve which comes to pass through the node< c goes to infinity 5', while the images of all the other curves of the sequence< c stay finite". By making this asymptotic construction, in turn, for different curves of the sequence, we will finally conclude the theorem.
