Michael P. Tuite

On genus two riemann surfaces formed from sewn tori

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

Torus n-Point Functions for \({\mathbb{R}}\) -graded Vertex Operator Superalgebras and Continuous Fermion Orbifolds

{\mathbb{H}_{2}}

Torus Chiral n-Point Functions for Free Boson and Lattice Vertex Operator Algebras

. Equivariance of these maps under certain subgroups of

Genus Two Partition and Correlation Functions for Fermionic Vertex Operator Superalgebras I

{Sp(4,\mathbb{Z})}

Virasoro Correlation Functions for Vertex Operator Algebras

is shown. The invertibility of both maps in a particular domain of