Adapted hyperbolic polygons and symplectic representations for group actions on Riemann surfaces

Autor:	Antonio Behn, Anita M. Rojas, Rubí E. Rodríguez
Rok vydání:	2013
Předmět:	Finite group Pure mathematics Algebra and Number Theory Riemann surface Fixed point Symplectic representation Moduli space Algebra symbols.namesake Group action symbols Abelian group Mathematics Symplectic geometry
Zdroj:	JOURNAL OF PURE AND APPLIED ALGEBRA Artículos CONICYT CONICYT Chile instacron:CONICYT
ISSN:	0022-4049
Popis:	We prove that given a finite group G together with a set of fixed geometric generators, there is a family of special hyperbolic polygons that uniformize the Riemann surfaces admitting the action of G with the given geometric generators. From these special polygons, we obtain geometric information for the action: a basis for the homology group of surfaces, its intersection matrix, and the action of the given generators of G on this basis. We then use the Frobenius algorithm to obtain a symplectic representation G of G corresponding to this action. The fixed point set of G in the Siegel upper half-space corresponds to a component of the singular locus of the moduli space of principally polarized abelian varieties. We also describe an implementation of the algorithm using the open source computer algebra system SAGE.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::3adb5c40a6595a0af85811e7affdf9a0 https://doi.org/10.1016/j.jpaa.2012.06.030 Zobrazit plný text záznamu Full Text from ScienceDirect