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arxiv: math/0402197 · v2 · pith:ND7ZPSWZnew · submitted 2004-02-12 · 🧮 math.GT · math.AG

Multiple Saddle Connections on Flat Surfaces and Principal Boundary of the Moduli Spaces of Quadratic Differentials

classification 🧮 math.GT math.AG
keywords moduliquadraticboundarydifferentialsspacedegenerationsdescribegeneric
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We describe typical degenerations of quadratic differentials thus describing ``generic cusps'' of the moduli space of meromorphic quadratic differentials with at most simple poles. The part of the boundary of the moduli space which does not arise from ``generic'' degenerations is often negligible in problems involving information on compactification of the moduli space. However, even for a typical degeneration one may have several short loops on the Riemann surface which shrink simultaneously. We explain this phenomenon, describe all rigid configurations of short loops, present a detailed description of analogs of desingularized stable curves arising here, and show how one can reconstruct a Riemann surface endowed with a quadratic differential which is close to a ``cusp'' by the corresponding point at the principal boundary.

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