Cohen-Macaulay modules over surface quasi-invariants and Calogero-Moser systems

Igor Burban, Alexander Zheglov

Published 2017-03-06Version 1

In this paper, we study algebras of surface quasi-invariants and prove that they are Cohen-Macaulay and Gorenstein in codimension one. Using the technique of matrix problems, we classify all Cohen-Macaulay modules of rank one over these algebras and determine their Picard groups. In terms of this classification, we describe the spectral module of a rational Calogero-Moser system of dihedral type. Finally, we elaborate the theory of the algebraic inverse scattering method, computing an explicit example of a deformed Calogero-Moser system.