Displaying similar documents to “A note on isolated points in the branch locus of the moduli space of compact Riemann surfaces.”

A remark on the homotopical dimension of some moduli spaces of stable Riemann surfaces

Gabriele Mondello (2008)

Journal of the European Mathematical Society

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Using a result of Harer, we prove certain upper bounds for the homotopical/cohomological dimension of the moduli spaces of Riemann surfaces of compact type, of Riemann surfaces with rational tails and of Riemann surfaces with at most k rational components. These bounds would follow from conjectures of Looijenga and Roth–Vakil.

Moduli stacks of polarized K3 surfaces in mixed characteristic

Rizov, Jordan (2006)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 14J28, 14D22. In this note we define moduli stacks of (primitively) polarized K3 spaces. We show that they are representable by Deligne-Mumford stacks over Spec(Z). Further, we look at K3 spaces with a level structure. Our main result is that the moduli functors of K3 spaces with a primitive polarization of degree 2d and a level structure are representable by smooth algebraic spaces over open parts of Spec(Z). To do this we use ideas...

Khinchin type condition for translation surfaces and asymptotic laws for the Teichmüller flow

Luca Marchese (2012)

Bulletin de la Société Mathématique de France

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We study a diophantine property for translation surfaces, defined in terms of saddle connections and inspired by classical Khinchin condition. We prove that the same dichotomy holds as in Khinchin theorem, then we deduce a sharp estimate on how fast the typical Teichmüller geodesic wanders towards infinity in the moduli space of translation surfaces. Finally we prove some stronger result in genus one.