The algebraic hull of the Kontsevich–Zorich cocycle

Abstract

We compute the algebraic hull of the Kontsevich–Zorich cocycle over any $ \mathrm {GL}^+_2(\mathbb {R}) $ invariant subvariety of the Hodge bundle, and derive from this finiteness results on such subvarieties.

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      booktitle = {Handbook of Dynamical Systems, {V}ol. 1{A}},
      pages = {1015--1089},
      publisher = {North-Holland, Amsterdam},
      year = {2002},
      mrclass = {37-02 (28D05 30F60 37A25 37D50 37F99)},
      mrnumber = {1928530},
      mrreviewer = {Richard Kenyon},
      doi = {10.1016/S1874-575X(02)80015-7},
      url = {https://doi.org/10.1016/S1874-575X(02)80015-7},
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      issn = {0020-9910},
      mrclass = {37D40 (32G15 58A35)},
      mrnumber = {3681397},
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      url = {https://doi.org/10.1007/s00222-017-0722-8},
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      mrclass = {37D40 (30F60 32G15)},
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      mrclass = {32G15 (30F60 37D40)},
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      doi = {10.2140/gt.2014.18.1323},
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      }
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      journal = {Geom. Topol.},
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      mrnumber = {3354955},
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    @INCOLLECTION{Zorich_survey,
      author = {Zorich, Anton},
      title = {Flat surfaces},
      booktitle = {Frontiers in Number Theory, Physics, and Geometry. {I}},
      pages = {437--583},
      publisher = {Springer, Berlin},
      year = {2006},
      mrclass = {37D40 (30F30 32G15 37D50 57M50)},
      mrnumber = {2261104},
      mrreviewer = {Thomas A. Schmidt},
      zblnumber = {1129.32012},
      }

Authors

Alex Eskin

University of Chicago, Chicago, IL

Simion Filip

Harvard University, Cambridge, MA

Alex Wright

Stanford University, Stanford, CA