Open Access
November 2017 Degenerations of Abelian differentials
Dawei Chen
Author Affiliations +
J. Differential Geom. 107(3): 395-453 (November 2017). DOI: 10.4310/jdg/1508551222


Consider degenerations of Abelian differentials with prescribed number and multiplicity of zeros and poles. Motivated by the theory of limit linear series, we define twisted canonical divisors on pointed nodal curves to study degenerate differentials, give dimension bounds for their moduli spaces, and establish smoothability criteria. As applications, we show that the spin parity of holomorphic and meromorphic differentials extends to distinguish twisted canonical divisors in the locus of stable pointed curves of pseudocompact type. We also justify whether zeros and poles on general curves in a stratum of differentials can be Weierstrass points. Moreover, we classify twisted canonical divisors on curves with at most two nodes in the minimal stratum in genus three. Our techniques combine algebraic geometry and flat geometry. Their interplay is a main flavor of the paper.

Funding Statement

During the preparation of this article the author was partially supported by the NSF CAREER Award DMS-1350396.


Download Citation

Dawei Chen. "Degenerations of Abelian differentials." J. Differential Geom. 107 (3) 395 - 453, November 2017.


Received: 4 June 2015; Published: November 2017
First available in Project Euclid: 21 October 2017

zbMATH: 06846968
MathSciNet: MR3715346
Digital Object Identifier: 10.4310/jdg/1508551222

Primary: 14H10 , 14H15 , 14K20

Keywords: Abelian differential , admissible cover , limit linear series , moduli space of curves , spin structure , translation surface , Weierstrass point

Rights: Copyright © 2017 Lehigh University

Vol.107 • No. 3 • November 2017
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