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Mason, G,Tuite, MP
2007
March
Communications In Mathematical Physics
On genus two Riemann surfaces formed from sewn tori
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()
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VERTEX OPERATOR-ALGEBRAS CONFORMAL FIELD-THEORIES 2-LOOP SUPERSTRINGS CENTRAL CHARGE
270
587
634
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 H-2. Equivariance of these maps under certain subgroups of Sp(4, Z) is shown. The invertibility of both maps in a particular domain of H-2 is also shown.
DOI 10.1007/s00220-006-0163-5
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