Abelian differentials with double zeros

Hershel M. Farkas

doi:10.1090/S0002-9939-1971-0274739-7

Abelian differentials with double zeros

Hershel M. Farkas^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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 ≧ 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.

Original language	English
Pages (from-to)	155-162
Number of pages	8
Journal	Proceedings of the American Mathematical Society
Volume	28
Issue number	1
DOIs	https://doi.org/10.1090/S0002-9939-1971-0274739-7
State	Published - Apr 1971
Externally published	Yes

Keywords

Abelian differentials
Riemann surfaces moduli
Theta functions

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10.1090/S0002-9939-1971-0274739-7

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AB - 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 ≧ 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.

KW - Abelian differentials

KW - Riemann surfaces moduli

KW - Theta functions

UR - https://www.scopus.com/pages/publications/84968513541

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Abelian differentials with double zeros

Abstract

Keywords

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