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- W2141869439 abstract "Let $Xrightarrow S$ be a smooth projective surjective morphism of relative dimension $n$, where $X$ and $S$ are integral schemes over $mathbb C$. Let $Lrightarrow X$ be a relatively very ample line bundle. For every sufficiently large positive integer $m$, there is a canonical isomorphism of the Deligne pairing $langle L ,cdots , Lranglerightarrow S$ with the determinant line bundle ${rm Det}((L- {mathcal O}_{X})^{otimes (n+1)}otimes L^{otimes m})$ cite{PRS}. If we fix a hermitian structure on $L$ and a relative Kahler form on $X$, then each of the line bundles ${rm Det}((L- {mathcal O}_{X})^{otimes (n+1)}otimes L^{otimes m})$ and $langle L, ,cdots, ,Lrangle$ carries a distinguished hermitian structure. We prove that the above mentioned isomorphism between $langle L, ,cdots, ,Lranglelongrightarrow S$ and ${rm Det}((L- {mathcal O}_{X})^{otimes (n+1)}otimes L^{otimes m})$ is compatible with these hermitian structures. This holds also for the isomorphism in cite{BSW} between a Deligne paring and a certain determinant line bundle." @default.
- W2141869439 created "2016-06-24" @default.
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- W2141869439 date "2015-01-12" @default.
- W2141869439 modified "2023-10-16" @default.
- W2141869439 title "Deligne pairing and Quillen metric" @default.
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