Vol. 71, No. 2, 1977

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On the Riemann-Roch equation for singular complex surfaces

Lawrence James Brenton

Vol. 71 (1977), No. 2, 299–312
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
Authors
Lawrence James Brenton