Rational orbits on three-symmetric products of Abelian varieties
Rational orbits on three-symmetric products of Abelian varieties
复制标题
阿贝尔簇三对称积的有理轨道
DOI：
10.1090/s0002-9947-1993-1106186-9
复制
发表时间：
1993
期刊：
影响因子：
--
通讯作者：
G. Pirola
中科院分区：
文献类型：
--
作者：
A. Alzati;G. Pirola
设A是n维Abel簇，n ≥ 2，CH 0（A）是A的零圈群，模有理等价，将一个有效的k次零圈作为Sk（A）（A的k-对称积）上的一个点，并考虑相应的有理等价类，得到一个映射γ：Sk（A）→ CH 0（A），其纤维称为γ-轨道.对任意n ≥ 2，本文确定了当k = 2或3时γ轨道的最大维数（它分别为1和2），以及γ-轨道族的最大维数，并对一般A作了一些改进，特别是证明了：当dim（A）≥ 4时，S3（A）不含任何γ-轨道;请注意，这意味着一般阿贝尔四重不包含任何三角曲线
Let A be an n-dimensional Abelian variety, n ≥ 2; let CH 0 (A) be the group of zero-cycles of A, modulo rational equivalence; by regarding an effective, degree k, zero-cycle, as a point on S k (A) (the k-symmetric product of A), and by considering the associated rational equivalence class, we get a map γ: S k (A) → CH 0 (A), whose fibres are called γ-orbits. For any n ≥ 2, in this paper we determine the maximal dimension of the γ-orbits when k = 2 or 3 (it is, respectively, 1 and 2), and the maximal dimension of families of γ-orbits; moreover, for generic A, we get some refinements and in particular we show that if dim(A) ≥ 4, S 3 (A) does not contain any γ-orbit; note that it implies that a generic Abelian four-fold does not contain any trigonal curve