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1. CMB 2003 (vol 46 pp. 429)
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The Grothendieck Trace and the de Rham Integral On a smooth $n$-dimensional complete variety $X$ over ${\mathbb C}$ we
show that the trace map ${\tilde\theta}_X \colon\break
H^n (X,\Omega_X^n)
\to {\mathbb C}$ arising from Lipman's version of Grothendieck duality
in \cite{ast-117} agrees with
$$
(2\pi i)^{-n} (-1)^{n(n-1)/2} \int_X \colon H^{2n}_{DR} (X,{\mathbb
C}) \to {\mathbb C}
$$
under the Dolbeault isomorphism.
Categories:14F10, 32A25, 14A15, 14F05, 18E30 |