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On Genus Two Riemann Surfaces Formed from Sewn Tori

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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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