Sixth Painlevé Equation, Universal Elliptic Curve, and Mirror of $\bold{P}^2$
Sixth Painlevé Equation, Universal Elliptic Curve, and Mirror of $\bold{P}^2$
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发表时间：
1996-05
影响因子：
1.4
通讯作者：
A. Khovanskii;A. Varchenko;V. Vassiliev;Y. Manin
中科院分区：
文献类型：
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作者：
A. Khovanskii;A. Varchenko;V. Vassiliev;Y. Manin
介绍了用于研究 Painleve VI 方程的代数几何设置。方程的哈密顿形式是在带有二阶标记点的通用椭圆曲线的扭曲相对余切丛上实现的。讨论了与椭圆函数理论和射影平面量子上同调的关系。
An algebro-geometric setting for the study of the Painleve VI equation is introduced. Hamiltonian form of the equation is realized on a twisted relative cotangent bundle to the universal elliptic curve with labelled points of order two. Relations with the theory of elliptic functions and the quantum cohomology of projective plane are discussed.