Connected components of strata of quadratic differentials over Teichmuller spaceConnected components of strata of quadratic differentials over Teichmuller space

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 Author Walker, Katharine C. Source arXiv.org Content type Text File Format PDF Date of Submission 2008-05-04 Language English
 Subject Domain (in DDC) Natural sciences & mathematics ♦ Mathematics Subject Keyword Mathematics - Geometric Topology ♦ Mathematics - Algebraic Geometry ♦ 30F30 (Primary) ♦ 14D20 (Secondary) ♦ math Abstract In this paper, we study connected components of strata of the space of quadratic differentials lying over $\T_g$. We use certain general properties of sections of line bundles to put a 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 we can state precisely the number of components. Educational Use Research Learning Resource Type Article Page Count 14