Symplectic Geometry of Moduli Spaces of Hurwitz Covers

  • We extend results by Mirzakhani in Maryam Mirzakhani. "Weil-Petersson volumes and intersection theory on the moduli space of curves." In: J. Amer. Math. Soc. (2007), pp. 1–23. to moduli spaces of Hurwitz covers. In particular we obtain equations relating Weil–Petersson volumes of moduli spaces of Hurwitz covers, Hurwitz numbers and certain Hurwitz cycles on Deligne–Mumford space related to those Riemann surfaces admitting Hurwitz covers of a specified branching profile. We state the precise orbifold structure of the moduli space of Hurwitz covers by applying ideas and results from Robbin–Salamon in Joel W. Robbin and Dietmar A. Salamon. "A construction of the Deligne–Mumford orbifold." In: J. Eur. Math. Soc. 8 (2006), pp. 611–699. Furthermore we prove compactness of the involved moduli spaces by applying SFT-compactness in the Cieliebak–Mohnke version from Kai Cieliebak and Klaus Mohnke. "Compactness for punctured holomorphic curves." In: Journal of Symplectic Geometry 3.4 (2005), pp.We extend results by Mirzakhani in Maryam Mirzakhani. "Weil-Petersson volumes and intersection theory on the moduli space of curves." In: J. Amer. Math. Soc. (2007), pp. 1–23. to moduli spaces of Hurwitz covers. In particular we obtain equations relating Weil–Petersson volumes of moduli spaces of Hurwitz covers, Hurwitz numbers and certain Hurwitz cycles on Deligne–Mumford space related to those Riemann surfaces admitting Hurwitz covers of a specified branching profile. We state the precise orbifold structure of the moduli space of Hurwitz covers by applying ideas and results from Robbin–Salamon in Joel W. Robbin and Dietmar A. Salamon. "A construction of the Deligne–Mumford orbifold." In: J. Eur. Math. Soc. 8 (2006), pp. 611–699. Furthermore we prove compactness of the involved moduli spaces by applying SFT-compactness in the Cieliebak–Mohnke version from Kai Cieliebak and Klaus Mohnke. "Compactness for punctured holomorphic curves." In: Journal of Symplectic Geometry 3.4 (2005), pp. 589–654.show moreshow less

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Metadaten
Author:Sven Prüfer
URN:urn:nbn:de:bvb:384-opus4-378402
Frontdoor URLhttps://opus.bibliothek.uni-augsburg.de/opus4/37840
Advisor:Kai Cieliebak
Type:Doctoral Thesis
Language:English
Year of first Publication:2017
Publishing Institution:Universität Augsburg
Granting Institution:Universität Augsburg, Mathematisch-Naturwissenschaftlich-Technische Fakultät
Date of final exam:2017/07/28
Release Date:2017/11/14
Tag:symplectic geometry; Hurwitz numbers; moduli spaces
GND-Keyword:Symplektische Geometrie; Modulraum; Hurwitz-Raum
Institutes:Mathematisch-Naturwissenschaftlich-Technische Fakultät
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Licence (German):Deutsches Urheberrecht