Baker-Akhiezer Modules on Rational Varieties

TL;DR

This paper constructs Baker-Akhiezer modules on rational varieties derived from complex projective spaces, demonstrating how meromorphic functions can be embedded into matrix differential operators in multiple variables.

Contribution

It introduces a method to build Baker-Akhiezer modules on specific rational varieties and shows their application in embedding meromorphic functions into matrix differential operators.

Findings

Existence of Baker-Akhiezer modules on rational varieties

Embedding of meromorphic function rings into matrix differential operators

Construction method applicable to varieties from projective spaces

Abstract

The free Baker-Akhiezer modules on rational varieties obtained from ${\mathbb C}P^{1}\times{\mathbb C}P^{n-1}$ 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.