Baker–Akhiezer Modules on the Intersections of Shifted Theta Divisors

  • Koji Cho

    Kyushu University, Fukuoka, Japan
  • Andrey Mironov

    Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russian Federation
  • Atsushi Nakayashiki

    Tsuda College, Tokyo, Japan


The restriction, on the spectral variables, of the Baker–Akhiezer (BA) module of a g-dimensional principally polarized abelian variety with the non-singular theta divisor to an intersection of shifted theta divisors is studied. It is shown that the restriction to a k-dimensional variety becomes a free module over the ring of di erential operators in k variables. The remaining g–k derivations de ne evolution equations for generators of the BA-module. As a corollary new examples of commutative rings of partial differential operators with matrix coecients and their non-trivial evolution equations are obtained.

Cite this article

Koji Cho, Andrey Mironov, Atsushi Nakayashiki, Baker–Akhiezer Modules on the Intersections of Shifted Theta Divisors. Publ. Res. Inst. Math. Sci. 47 (2011), no. 2, pp. 553–567

DOI 10.2977/PRIMS/43