Baker-Akhiezer Modules on Rational Varieties

Abstract

Abstract. The free Baker-Akhiezer modules on rational varieties obtained from CP 1 × CP n−1 by identification of two hypersurfaces are constructed. The corollary of this construction is the existence of embedding of meromorphic function ring with some fixed pole into the ring of matrix differential operators in n variables.

Discretization of Baker–Akhiezer modules and commuting difference operators in several discrete variables

“…, t g ). Moreover we choose parameters (α, β), (α i , β i ) in general position, which means that the parameters belong to some open domain (see [12] to specify this domain). According to (8) the equation…”

“…Let us fix Λ ∈ C * . The discrete Baker-Akhiezer moduleM Λ is similarly defined to the case of Abelian varieties as the discretization of the Baker-Akhiezer module constructed in [12]. It is defined directly bŷ…”

“…The equation (29) is equivalent to the system of linear homogeneous equations for {h jα }. As shown in [12] ♯{h jα } − ♯{equations} = g g + k − 1 g ,…”

“…Thus M Λ and grM Λ become modules over the ring of differential operators D := K[∂ 1 , ..., ∂ g ], where ∂ i acts by ∇ i . The D module M Λ is the Baker-Akhiezer module of (Γ, (f = 0)) constructed in [12].…”

“…where ∂ i acts by ∇ i . The D module M Λ is the Baker-Akhiezer module of (Γ, (f = 0)) constructed in [12].…”