Selecta Mathematica

, Volume 24, Issue 1, pp 187–225 | Cite as

Towards a cluster structure on trigonometric zastava

  • Michael FinkelbergEmail author
  • Alexander Kuznetsov
  • Leonid Rybnikov
  • Galyna Dobrovolska


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.

Mathematics Subject Classification

13F60 14M15 


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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  • Michael Finkelberg
    • 1
    • 2
    Email author
  • Alexander Kuznetsov
    • 3
    • 4
    • 5
  • Leonid Rybnikov
    • 1
    • 6
  • Galyna Dobrovolska
    • 7
  1. 1.Department of MathematicsNational Research University Higher School of Economics, Russian FederationMoscowRussia
  2. 2.Skolkovo Institute of Science and TechnologyMoscowRussia
  3. 3.Algebraic Geometry SectionSteklov Mathematical InstituteMoscowRussia
  4. 4.Laboratory of Algebraic GeometryNational Research University Higher School of Economics, Russian FederationMoscowRussia
  5. 5.The Poncelet LaboratoryIndependent University of MoscowMoscowRussia
  6. 6.Institute for the Information Transmission Problems of RASMoscowRussia
  7. 7.Department of MathematicsColumbia UniversityNew YorkUSA

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