On the Riemann-Roch equation for singular complex surfaces

Grothendieck-riemann-roch and the Moduli of Enriques Surfaces

A (complex) Enriques surface is a projective smooth connected algebraic surface Y over C with H(Y,OY ) = H (Y,OY ) = (0), (Ω 2 Y ) ⊗ 2 ≃ OY but Ω 2 Y 6≃ OY ([CF]). In this note we give a short proof of the fact that the coarse moduli space of complex Enriques surfaces is quasi-affine. This was first shown by Borcherds [B] using the denominator function of a generalized Kac-Moody superalgebra (t...

A Riemann-roch Theorem for One-dimensional Complex Groupoids

We consider a smooth groupoid of the form Σ ⋊ Γ where Σ is a Riemann surface and Γ a discrete pseudogroup acting on Σ by local conformal diffeomorphisms. After defining a K-cycle on the crossed product C0(Σ) ⋊ Γ generalising the classical Dolbeault complex, we compute its Chern character in cyclic cohomology, using the index theorem of Connes and Moscovici. This involves in particular a general...

Complex Analysis on Riemann Surfaces

Complex Analysis on Riemann Surfaces

Complex Analysis on Riemann Surfaces