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Algèbre de Rees et Fibre spéciale

Abstract : This work is at the same time in Algebraic Geometry and Commutative Algebra. The first part of this thesis studies the Rees ring (blow--up ring) and the fiber cone of a lattice ideal of codimenson 2 in a polynomial rings. In the case where the ideal is generated by three or four elements, the defining equations of the Rees ring can be described explicitly. In the general case, we define the graph of syzygies of the ideal, and study it combinatorially. We obtain: 1/ The dimension of the fiber cone is 2 or 3. 2/ If the ideal is not a complete intersection, then the fiber cone is Cohen--Macaulay of dimension 3, reduced, of minimal degree, i.e the fiber cone has remarkable geometrical properties. An explicit presentation of the fiber cone is also given. 3/ The Rees ring is a Cohen--Macaulay ring generated by forms of degree at most 2. The second part of this thesis concerns the simplicial ideals introduced by Mr. Morales. Using combinatorial properties, we give a large class of binomial simplicial ideals with reduction number 1.
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Contributor : Minh Lam Ha <>
Submitted on : Monday, October 15, 2007 - 2:43:18 PM
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  • HAL Id : tel-00179342, version 1



Minh Lam Ha. Algèbre de Rees et Fibre spéciale. Mathématiques [math]. Université Joseph-Fourier - Grenoble I, 2006. Français. ⟨tel-00179342⟩



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