English

Towards a cluster structure on trigonometric zastava

Algebraic Geometry 2018-09-05 v5 Quantum Algebra Representation Theory

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.

Keywords

Cite

@article{arxiv.1504.05605,
  title  = {Towards a cluster structure on trigonometric zastava},
  author = {Michael Finkelberg and Alexander Kuznetsov and Leonid Rybnikov and Galyna Dobrovolska},
  journal= {arXiv preprint arXiv:1504.05605},
  year   = {2018}
}

Comments

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

R2 v1 2026-06-22T09:20:08.037Z