Group actions on Jacobian varieties
| Autor: | Anita M. Rojas |
|---|---|
| Rok vydání: | 2007 |
| Předmět: |
Pure mathematics
Geometric function theory 14L30 General Mathematics Lattice (group) Jacobian variety Jacobian varieties Riemann Xi function group actions geometric signature Mathematics - Algebraic Geometry symbols.namesake Riemann sum FOS: Mathematics Algebraic Geometry (math.AG) 14H40 20C05 Mathematics Isogeny Riemann surface Algebra Riemann surfaces Uniformization theorem Riemann's existence theorem symbols |
| Zdroj: | Rev. Mat. Iberoamericana 23, no. 2 (2007), 397-420 |
| ISSN: | 0213-2230 |
| Popis: | Consider a finite group $G$ acting on a Riemann surface $S$, and the associated branched Galois cover $\pi_G:S \to Y=S/G$. We introduce the concept of geometric signature for the action of $G$, and we show that it captures the information of the geometric structure of the lattice of intermediate covers, the information about the isotypical decomposition of the rational representation of the group $G$ acting on the Jacobian variety $JS$ of $S$, and the dimension of the subvarieties of the isogeny decomposition of $JS$. We also give a version of Riemann's existence theorem, adjusted to the present setting. Comment: 23 pages. Minor grammatical changes and a corrected version of the last corollary |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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