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Limits of Real-Normalized Dierentials on Stable Curves

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dc.contributor.advisor Grushevsky, Samuel en_US
dc.contributor.author Norton, Chaya Rifka en_US
dc.contributor.other Department of Mathematics en_US
dc.date.accessioned 2017-09-20T16:50:10Z
dc.date.available 2017-09-20T16:50:10Z
dc.date.issued 2014-12-01 en_US
dc.identifier.uri http://hdl.handle.net/11401/76407 en_US
dc.description 115 pgs en_US
dc.description.abstract A recent approach proposed by Grushevsky and Krichever uses real-normalized differentials, meromorphic differentials with all periods real, to study the geometry of the moduli space of curves. We describe the behavior of real-normalized differentials under degeneration of the Riemann surface, and this analysis allows us to study the limits of zeros of these differentials near the boundary of the Deligne-Mumford compactification of the moduli space of curves. Our explicit description of the behavior of real-normalized differentials near nodal curves provides a tool for understanding common zeros of such differentials which has applications for the study of plane curves. This analysis should have further applications to degenerations of holomorphic differentials which is of interest in Teichmueller dynamics. en_US
dc.description.sponsorship This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree. en_US
dc.format Monograph en_US
dc.format.medium Electronic Resource en_US
dc.language.iso en_US en_US
dc.publisher The Graduate School, Stony Brook University: Stony Brook, NY. en_US
dc.subject.lcsh Mathematics en_US
dc.title Limits of Real-Normalized Dierentials on Stable Curves en_US
dc.type Dissertation en_US
dc.mimetype Application/PDF en_US
dc.contributor.committeemember Lazarsfeld, Robert en_US
dc.contributor.committeemember Takhtajan, Leon en_US
dc.contributor.committeemember Wolpert, Scott en_US

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