Towards a cluster structure on trigonometric zastava

Abstract

We study a moduli problem on a nodal curve of arithmetic genus 1, whose solution is an open subscheme in the zastava space for projective line. This moduli space is equipped with a natural Poisson structure, and we compute it in a natural coordinate system. We compare this Poisson structure with the trigonometric Poisson structure on the transversal slices in an affine flag variety. We conjecture that certain generalized minors give rise to a cluster structure on the trigonometric zastava.

Main text by M. Finkelberg, A. Kuznetsov and L. Rybnikov with an appendix by G. Dobrovolska; v3 32 pages, Proof of Proposition 4.3 corrected, Section 1.5 added; v4 33 pages, the final version to appear in Selecta Math.; v5 the published version