Towards a cluster structure on trigonometric zastava

• Michael Finkelberg ^[1] ; Alexander Kuznetsov ^[2] ; Leonid Rybnikov ^[1] ; Galyna Dobrovolska ^[3]
  1. [1] Higher School of Economics, National Research University

     Higher School of Economics, National Research University

     Rusia

     
  2. [2] Steklov Mathematical Institute

     Steklov Mathematical Institute

     Rusia

     
  3. [3] Columbia University

     Columbia University

     Estados Unidos

     

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• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 24, Nº. 1, 2018, págs. 187-225
• Idioma: inglés
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• Resumen

  • 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.