Vol. 4, No. 4, 2019

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A Dolbeault–Hilbert complex for a variety with isolated singular points

John Lott

Vol. 4 (2019), No. 4, 707–720

Given a compact Hermitian complex space with isolated singular points, we construct a Dolbeault-type Hilbert complex whose cohomology is isomorphic to the cohomology of the structure sheaf. We show that the corresponding K-homology class coincides with the one constructed by Baum, Fulton and MacPherson.

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Dolbeault, singular, variety, Riemann–Roch
Mathematical Subject Classification 2010
Primary: 19K33, 19L10, 32W05, 58J10
Received: 23 April 2019
Revised: 20 June 2019
Accepted: 11 July 2019
Published: 10 January 2020
John Lott
Department of Mathematics
University of California
Berkeley, CA
United States