Prymians of real curves and their applications to the effectivization of Schrödinger operators (Q1824095)

\textit{A. P. Veselov} and \textit{S. P. Novikov} [Sov. Math., Dokl. 30, 588- 591 (1984); translation from Dokl. Akad. Nauk SSSR 279, 20-24 (1984; Zbl 0613.35020); and ibid., 705-708 (1984); translation from Dokl. Akad. Nauk SSSR 279, 784-788 (1984; Zbl 0602.35024)] describe the class of real two- dimensional Schrödinger operators \[ L=\partial {\bar \partial}+2\partial {\bar \partial} \ell n \theta (zU_ 1+\bar zU_ 2- e| V)-\epsilon_ 0, \] where \(\theta\) denotes Prym's theta-function of real algebraic curve with involutions. Present paper gives the effective description of Prym's variety of real curves and special properties of holomorphical differentials on real curves.