UNIQUENESS OF AFFINE STRUCTURES ON RIEMANN SURFACES
| Autor: | John T. Masterson |
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| Rok vydání: | 1992 |
| Předmět: | |
| Zdroj: | Tamkang Journal of Mathematics. 23:87-94 |
| ISSN: | 2073-9826 0049-2930 |
| Popis: | Let $M$ be any compact Riemann surface of genus $g\ge 2$. It is first established that there do not exist on $M$ any generic low- degree simple polar variations of branched affine structures having fixed nonpolar and polar branch data and fixed induced character homomorphism $\tilde \psi$. Hence, these structures depend uniquely on the branch data and the homomorphism. A related result is also established concerning the nonexistence on $M$ of generic low-degree single-point variations of branched affine structures having fixed homomorphism $\tilde \psi$. These resuits depend on the Noether and Weierstrass gaps on $M$. Corollaries are derived concerning mappings induced by sections of vector bundles of affine structures and concerning structures on an arbitrary hyperelliptic or elliptic ($g =1$) surface $M$. |
| Databáze: | OpenAIRE |
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