On Genus Two Riemann Surfaces Formed from Sewn Tori

We describe the period matrix and other data on a higher genus Riemann nsurface in terms of data coming from lower genus surfaces via an explicit nsewing procedure. We consider in detail the construction of a genus two Riemann nsurface by either sewing two punctured tori together or by sewing a ntwice-punctured torus to itself. In each case the genus two period matrix is nexp..