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.…

