The canonical lifting of an ordinary Jacobian variety need not be a Jacobian variety
The canonical lifting of an ordinary Jacobian variety need not be a Jacobian variety
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普通雅可比簇的规范提升不一定是雅可比簇
DOI：
10.2969/jmsj/03830427
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发表时间：
1986
影响因子：
0.7
通讯作者：
T. Sekiguchi
中科院分区：
文献类型：
--
作者：
F. Oort;T. Sekiguchi
请注意，如果$g\leqq 3$，则问题的答案是肯定的，因为通过A。Weil对于$g=2$（cf. [15]，p. 37，Satz 2），and by Oort-Ueno for $g\leqq 3$（cf. [10])我们知道，在这种情况下，一个主要的极化阿贝尔品种是雅可比。在这一注记中，我们表明，在一般情况下，这个问题的答案是否定的（参见。林前2.5下面，cf。注2.6）。第二提交人衷心感谢乌得勒支大学的盛情款待和良好的工作条件。
Note that the answer to the problem is affirmative if $g\leqq 3$ , because by A. Weil for $g=2$ (cf. [15], p. 37, Satz 2), and by Oort-Ueno for $g\leqq 3$ (cf. [10]), we know that in this case a principally polarized abelian variety is a Jacobian. In this note we show that in general the answer to the problem is negative (cf. Cor. 2.5 below, also cf. Remark 2.6). The second author would like to express his hearty thanks to the University of Utrecht for hospitality and for excellent working conditions.