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Theses

La trace en géométrie projective et torique.

Abstract : We present in the first part an algebraic residual characterization
of usual trace-forms on local analytic hypersurfaces. We thus obtain a stronger version of the Abel-inverse theorem by Passare and Henkin in projective space and we relate it to the theorem by Wood on the algebraicity of local analytic hypersurfaces. We show how those inversion theorems can be anderstood as a rigidity propriety of a particular differential system linked to the wave choc
equation and we obtain a new method to compute the dimension of the vector space of abelian forms of maximal degree on a projective hypersurface.
The second part begins with a combinatorial characterization of satisfactory families of line bundles on a smooth complete toric variety to obtain an intrinsec notion of toric concavity allowing a toric generalisation of the trace. The use of toric residues and residue currents permits to show a toric version of Wood's and inverse Abel's theorem, providing a more precise description of the defining
polynomial in the hypersurface case.
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https://tel.archives-ouvertes.fr/tel-00136109
Contributor : Martin Weimann <>
Submitted on : Tuesday, March 13, 2007 - 3:30:56 PM
Last modification on : Monday, April 27, 2020 - 4:14:03 PM
Long-term archiving on: : Friday, September 21, 2012 - 12:50:11 PM

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  • HAL Id : tel-00136109, version 1

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Martin Weimann. La trace en géométrie projective et torique.. Mathématiques [math]. Université Sciences et Technologies - Bordeaux I, 2006. Français. ⟨tel-00136109⟩

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