编辑Jacobians的4-Theta嵌入
Edited 4-Theta embeddings of Jacobians
摘要：
利用Lefschetz嵌入定理，将主极化$g$维阿贝尔簇簇通过$4^g$半特征θ函数的线性系嵌入到射影空间中.假设我们{ \em edit}这个线性系，通过丢弃所有在原点消失的θ函数，使其阶数大于大于奇偶性要求。我们证明了对于雅可比行列式，编辑后的$4Θ$线性系仍然定义了到射影空间的嵌入。此外，我们证明了投影模型的雅可比矩阵所产生的基本建设的雅可比矩阵最近给出的作者（通过线性外壳后）的副本编辑$4Θ$模型。因此，对于所有紧致黎曼曲面，我们以一种新的方式将代数雅可比行列式和解析雅可比行列式联系在一起。
英文摘要：
By the Lefschetz embedding theorem, a principally polarized $g$-dimensional abelian variety is embedded into projective space by the linear system of $4^g$ half-characteristic theta functions. Suppose we {\em edit} this linear system by dropping all the theta functions vanishing at the origin to order greater than parity requires. We prove that for Jacobians the edited $4Θ$ linear system still defines an embedding into projective space. Moreover, we prove that the projective models of Jacobians arising from the elementary construction of Jacobians recently given by the author are (after passage to linear hulls) copies of the edited $4Θ$ model. Thus, for all compact Riemann surfaces, we tie together algebraic and analytic Jacobians in a new way.
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