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The Grothendieck Trace and the de Rham Integral

Published online by Cambridge University Press:  20 November 2018

Pramathanath Sastry  and
Yue Lin L. Tong
Pramathanath Sastry
Affiliation:
University of Toronto at Mississauga Mississauga, Ontario, email: [email protected]
Yue Lin L. Tong
Affiliation:
Purdue University West Lafayette, IN USA, email: [email protected]
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Abstract

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On a smooth $n$-dimensional complete variety $X$ over $\mathbb{C}$ we show that the trace map ${{\bar{\theta }}_{X}}\,:\,{{H}^{n}}(X,\,\Omega _{X}^{n})\,\to \,\mathbb{C}$ arising from Lipman's version of Grothendieck duality in $\left[ \text{L} \right]$ agrees with

$${{(2\pi i)}^{-n}}{{(-1)}^{n(n-1)/2}}\,\int_{X}{:\,H_{DR}^{2n}\,(X,\,\mathbb{C})\,\to \,\mathbb{C}}$$

under the Dolbeault isomorphism.

Keywords

14F1032A2514A1514F0518E30
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 46 , Issue 3 , 01 September 2003 , pp. 429 - 440
Copyright
Copyright © Canadian Mathematical Society 2003

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