Moduli Spaces of Isoperiodic Forms on Riemann Surfaces

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Moduli Spaces of Isoperiodic Forms on Riemann Surfaces

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Title: Moduli Spaces of Isoperiodic Forms on Riemann Surfaces
Author: McMullen, Curtis T.
Citation: McMullen, Curtis T. 2012. “Moduli Spaces of Isoperiodic Forms on Riemann Surfaces.” Working paper, Department of Mathematics, Harvard University.
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Abstract: This paper describes the intrinsic geometry of a leaf \(\mathcal{A}(L)\) of the absolute period foliation of the Hodge bundle \(\Omega \bar{M}_g\): its singular Euclidean structure, its natural foliations and its discretized Teichmuller dynamics. We establish metric completeness of \(\mathcal{A}(L)\) for general g, and then turn to a study of the case g = 2. In this case the Euclidean structure comes from a canonical meromorphic quadratic differential on \(\mathcal{A}(L) \cong \mathbb{H}\), whose zeros, poles and exotic trajectories are analyzed in detail.
Terms of Use: This article is made available under the terms and conditions applicable to Open Access Policy Articles, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#OAP
Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:11880197
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