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Towards a cluster structure on trigonometric zastava

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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.

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Authors and Affiliations

  1. Department of Mathematics, National Research University Higher School of Economics, Russian Federation, 6 Usacheva st, Moscow, Russia, 119048

    Michael Finkelberg & Leonid Rybnikov

  2. Skolkovo Institute of Science and Technology, Moscow, Russia

    Michael Finkelberg

  3. Algebraic Geometry Section, Steklov Mathematical Institute, 8 Gubkina, Moscow, Russia, 119991

    Alexander Kuznetsov

  4. Laboratory of Algebraic Geometry, National Research University Higher School of Economics, Russian Federation, Moscow, Russia

    Alexander Kuznetsov

  5. The Poncelet Laboratory, Independent University of Moscow, Moscow, Russia

    Alexander Kuznetsov

  6. Institute for the Information Transmission Problems of RAS, Moscow, Russia

    Leonid Rybnikov

  7. Department of Mathematics, Columbia University, 2990 Broadway, New York, NY, 10027, USA

    Galyna Dobrovolska

Authors
  1. Michael Finkelberg
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  2. Alexander Kuznetsov
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  3. Leonid Rybnikov
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  4. Galyna Dobrovolska
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Corresponding author

Correspondence to Michael Finkelberg.

Additional information

To Sasha Beilinson with love and gratitude.

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Finkelberg, M., Kuznetsov, A., Rybnikov, L. et al. Towards a cluster structure on trigonometric zastava. Sel. Math. New Ser. 24, 187–225 (2018). https://doi.org/10.1007/s00029-016-0287-1

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  • DOI: https://doi.org/10.1007/s00029-016-0287-1

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