On the Riemann-Roch equation for singular complex surfaces

Lawrence James Brenton

Vol. 71 (1977), No. 2, 299–312

DOI: 10.2140/pjm.1977.71.299

Abstract

An explicit constructive algorithm is developed for calculating the Hirzebruch-Riemann-Roch index χ(L) = ∑ _i=0²(−1)ⁱ dimHⁱ(X,𝒪(L)) of a holomorphic line bundle L on a normal compact two-dimensional complex analytic space (X,𝒪) with singularities, in terms of the standard global topological invariants of X and a “correction term” involving only the local analytic and topological structure of the singular points themselves. The technique is by resolutious of singularities.

Mathematical Subject Classification 2000

Primary: 32J15

Milestones

Received: 29 December 1976

Revised: 16 March 1977

Published: 1 August 1977