Connected components of the strata of quadratic differentials over the Teichmüller space

In this paper, we study the connected components of strata of the space of quadratic differentials lying over the Teichmüller space. We use certain general properties of sections of line bundles to put an upper bound on the number of connected components, and a generalized version of the Gauss map a...

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Bibliographic Details
Published in:Geometriae dedicata 2009-10, Vol.142 (1), p.47-60
Main Author: Walker, Katharine C.
Format: Article
Language:English
Subjects:
Algebraic Geometry
Convex and Discrete Geometry
Differential Geometry
Hyperbolic Geometry
Mathematics
Mathematics and Statistics
Original Paper
Projective Geometry
Topology
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Summary:In this paper, we study the connected components of strata of the space of quadratic differentials lying over the Teichmüller space. We use certain general properties of sections of line bundles to put an upper bound on the number of connected components, and a generalized version of the Gauss map as an invariant to put a lower bound on the number of such components. For strata with sufficiently many zeroes of the same order the above lower bound and upper bound coincide.
ISSN:0046-5755
1572-9168
DOI:10.1007/s10711-009-9357-2