## On Genus Two Riemann Surfaces Formed from Sewn Tori

dc.contributor.author | Mason, Geoffrey | |

dc.contributor.author | Tuite, Michael P. | |

dc.date.accessioned | 2012-01-09T13:44:07Z | |

dc.date.available | 2012-01-09T13:44:07Z | |

dc.date.issued | 2006 | |

dc.identifier.citation | Geoffrey Mason and Michael P. Tuite(2006)On Genus Two Riemann Surfaces Formed from Sewn Tori, Commun.Math.Phys. 270 (2007) 587-634 | en_US |

dc.identifier.uri | http://hdl.handle.net/10379/2450 | |

dc.description.abstract | We describe the period matrix and other data on a higher genus Riemann surface in terms of data coming from lower genus surfaces via an explicit sewing procedure. We consider in detail the construction of a genus two Riemann surface by either sewing two punctured tori together or by sewing a twice-punctured torus to itself. In each case the genus two period matrix is explicitly described as a holomorphic map from a suitable domain (parameterized by genus one moduli and sewing parameters) to the Siegel upper half plane $\mathbb{H}_{2}$. Equivariance of these maps under certain subgroups of $Sp(4,\mathbb{Z)}$ is shown. The invertibility of both maps in a particular domain of $\mathbb{H}_{2}$ is also shown. | |

dc.format | application/pdf | en_US |

dc.language.iso | en | en_US |

dc.subject | Mathematics - Quantum Algebra | |

dc.subject | High Energy Physics - Theory | |

dc.subject | Mathematics - Complex Variables | |

dc.title | On Genus Two Riemann Surfaces Formed from Sewn Tori | en_US |

dc.type | Article | en_US |

dc.local.publishedsource | http://arxiv.org/pdf/math/0603088 | en_US |

dc.description.peer-reviewed | peer-reviewed | en_US |

dc.local.authors | Geoffrey Mason and Michael P. Tuite | |

dc.local.arxivid | math/0603088 | |

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