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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.

References [Enhancements On Off] (What's this?)

  • [F1] . Hershel M. Farkas, Special divisors and analytic subloci of Teichmueller space, Amer. J. Math. 88 (1966), 881-901. MR 35 #4406. MR 0213546 (35:4406)
  • [F2] . -, On the Schottky relation and its generalization to arbitrary genus, Ann. of Math. (to appear).
  • [L] . Joseph Lewittes, Riemann surfaces and the theta function, Acta Math. 111 (1964), 37-61. MR 28 #206. MR 0156964 (28:206)
  • [R] . Harry E. Rauch, Functional independence of theta constants, Bull. Amer. Math. Soc. 74 (1968), 633-638. MR 37 #1590. MR 0226000 (37:1590)
  • [SG] . G. Sansone and J. Gerretsen, Lectures on the theory of functions of a complex variable, Noordhoff Groningen, 1960. MR 22 #4819. MR 0113988 (22:4819)

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Keywords: Abelian differentials, theta functions, Riemann surfaces moduli
Article copyright: © Copyright 1971 American Mathematical Society

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