标题： 阿贝尔-普里姆映射在存在额外对合情况下的逆 显示英文标题

标题： Inversion of the Abel--Prym map in presence of an additional involution

摘要： 与黎曼曲面对称幂到其雅可比簇的阿贝尔映射不同，阿贝尔-普里姆映射通常不能通过与雅可比逆问题相关的传统技术及其主要组成部分，即黎曼消去定理来逆转。这是因为相应的黎曼消去定理的对应物给出的点数是普里姆流形维度的两倍。然而，如果黎曼曲面有一个与定义普里姆流形的对合交换的第二个对合，并且满足某种附加条件，则可以定义一个雅可比逆问题的类似物，并用普里姆θ函数来表示。我们提出了这些条件，并将满足它们的对合对称为第一类对合对。我们给出了对合对成为第一类对合对的必要条件，并给出了一系列具有此类对合对的曲线的例子，主要是Hitchin系统的谱曲线，以及Kovalewski系统的谱曲线。 显示英文摘要

摘要： Unlike Abel map of the symmetric power of a Riemann surface onto its Jacobian, the Abel--Prym map generically can not be reversed by means of conventional technique related to the Jacobi inversion problem, and of its main ingredient, namely the Riemann vanishing theorem. It happens because the corresponding analog of the Riemann vanishing theorem gives twice as many points as the dimension of the Prym variety. However, if the Riemann surface has a second involution commuting with the one defining the Prym variety and satisfying a certain additional condition, an analog of the Jacobi inversion can be defined, and expressed in terms of the Prym theta function. We formulate these conditions and refer to the pairs of involutions satisfying them as to pairs of the first type. We formulate necessary conditions for the pair of involutions to be a pair of the first type, and give a series of examples of curves with such pairs of involutions, mainly spectral curves of Hitchin systems, and also a spectral curve of the Kovalewski system.