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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Abelian differentials with double zeros
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by Hershel M. Farkas PDF
Proc. Amer. Math. Soc. 28 (1971), 155-162 Request permission

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
  • © Copyright 1971 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 28 (1971), 155-162
  • MSC: Primary 30.45
  • DOI: https://doi.org/10.1090/S0002-9939-1971-0274739-7
  • MathSciNet review: 0274739