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15 September 2008 Linear manifolds in the moduli space of one-forms
Martin Möller
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Duke Math. J. 144(3): 447-487 (15 September 2008). DOI: 10.1215/00127094-2008-041

Abstract

We study closures of GL2+(R)-orbits in the total space ΩMg of the Hodge bundle over the moduli space of curves under the assumption that they are algebraic manifolds. We show that in the generic stratum, such manifolds are the whole stratum, the hyperelliptic locus, or parameterize curves whose Jacobian has additional endomorphisms. This follows from a cohomological description of the tangent bundle to ΩMg. For nongeneric strata, similar results can be shown by a case-by-case inspection. We also propose to study a notion of linear manifold that comprises Teichmüller curves, Hilbert modular surfaces, and the ball quotients of Deligne and Mostow [DM]. Moreover, we give an explanation for the difference between Hilbert modular surfaces and Hilbert modular threefolds with respect to this notion of linearity

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Martin Möller. "Linear manifolds in the moduli space of one-forms." Duke Math. J. 144 (3) 447 - 487, 15 September 2008. https://doi.org/10.1215/00127094-2008-041

Information

Published: 15 September 2008
First available in Project Euclid: 15 August 2008

zbMATH: 1148.32007
MathSciNet: MR2444303
Digital Object Identifier: 10.1215/00127094-2008-041

Subjects:
Primary: 32G15
Secondary: 14D07 , 32G20

Rights: Copyright © 2008 Duke University Press

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Vol.144 • No. 3 • 15 September 2008
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