Singular abelian surfaces and binary quadratic forms
Singular abelian surfaces and binary quadratic forms
复制标题
奇异阿贝尔曲面和二元二次形式
DOI：
10.1007/bfb0066163
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发表时间：
1974
影响因子：
1.4
通讯作者：
Naoki Mitani
中科院分区：
文献类型：
--
作者：
T. Shioda;Naoki Mitani
奇异阿贝尔曲面是指一个2维的复阿贝尔簇，其皮卡数等于最大可能值4。本文证明了关于SL ~ 2（~）的奇异交换曲面与正定偶整二元二次型的等价类一一对应（定理3.1）。由于这种分类，每一个奇异的阿贝尔曲面原来是两个椭圆曲线的产品。
By a singular abelian surface we mean a complex abelian variety of dimension 2 whose Picard number is equal to the maximum possible value 4. In this note we prove that singular abelian surfaces are in one-to-one correspondence with equivalence classes of positive definite even integral binary quadratic forms with respect to SL2 (~)(Theorem 3.1). As a consequence of this classification, every singular abelian surface turns out to be a product of two elliptic curves.