Duke Mathematical Journal

Moduli spaces of isoperiodic forms on Riemann surfaces

Curtis T. McMullen

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Abstract

This paper describes the intrinsic geometry of a leaf A(L) of the absolute period foliation of the Hodge bundle ΩM¯g: its singular Euclidean structure, its natural foliations, and its discretized Teichmüller dynamics. We establish metric completeness of 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 A(L)H whose zeros, poles, and exotic trajectories are analyzed in detail.

Article information

Source
Duke Math. J., Volume 163, Number 12 (2014), 2271-2323.

Dates
First available in Project Euclid: 15 September 2014

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1410789516

Digital Object Identifier
doi:10.1215/00127094-2785588

Mathematical Reviews number (MathSciNet)
MR3263035

Zentralblatt MATH identifier
1371.30037

Subjects
Primary: 30F30: Differentials on Riemann surfaces

Citation

McMullen, Curtis T. Moduli spaces of isoperiodic forms on Riemann surfaces. Duke Math. J. 163 (2014), no. 12, 2271--2323. doi:10.1215/00127094-2785588. https://projecteuclid.org/euclid.dmj/1410789516


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