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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Abelian differentials with double zeros


Author: Hershel M. Farkas
Journal: Proc. Amer. Math. Soc. 28 (1971), 155-162
MSC: Primary 30.45
MathSciNet review: 0274739
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Abstract: In this note we give a simple proof of the following theorem: The locus of points in the Torelli space of compact Riemann surfaces of genus $ g \geqq 2$ whose underlying surfaces do not permit a basis for the abelian differentials of first kind each of whose elements is a differential with double zeros, has positive codimension in the Torelli space.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0274739-7
PII: S 0002-9939(1971)0274739-7
Keywords: Abelian differentials, theta functions, Riemann surfaces moduli
Article copyright: © Copyright 1971 American Mathematical Society