Deligne pairing and determinant bundle

Indranil Biswas; Georg Schumacher; Lin Weng

doi:10.3934/era.2011.18.91

Article Contents

2011, Volume 18: 91-96. Doi: 10.3934/era.2011.18.91

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Deligne pairing and determinant bundle

1.
School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005
2.
Fachbereich Mathematik und Informatik, Philipps-Universität Marburg, Lahnberge, Hans-Meerwein-Strasse, D-35032 Marburg
3.
Graduate School of Mathematics, Kyushu University Fukuoka, 819-0395

Received: February 28, 2011

Revised: May 31, 2011

Published: December 2010

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Abstract

Let $X \rightarrow\ S$ be a smooth projective surjective morphism, where $X$ and $S$ are integral schemes over $\mathbb C$. Let $L_0\, L_1\, \cdots \, L_{n-1}\, L_{n}$ be line bundles over $X$. There is a natural isomorphism of the Deligne pairing 〈$L_0\, \cdots\, L_{n}$〉with the determinant line bundle $Det(\otimes_{i=0}^{n} (L_i- \mathcal O_{X}))$.

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Mathematics Subject Classification: Primary: 14F05; Secondary: 14D06.

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