Geometry of toric varieties by Michel Brion, Laurent Bonavero

By Michel Brion, Laurent Bonavero

Résumé :
Géométrie des variétés toriques
Ce quantity rassemble des textes issus de l'école d'été « Géométrie des variétés toriques » (Grenoble, 19 juin-7 juillet 2000). Ils reprennent, sous une forme plus détaillée, des cours et des exposés de séminaire des deuxième et troisième semaines de l'école, l. a. première semaine ayant été consacrée à des cours introductifs. On trouvera dans l'article de D. Cox un landscape des travaux récents en géométrie torique et de leurs purposes, qui met en standpoint les autres textes du présent volume.

Mots clefs : Variétés toriques

Abstract:
This quantity gathers texts originated in the summertime institution ``Geometry of Toric Varieties'' (Grenoble, June 19-July 7, 2000). those are accelerated types of lectures brought in the course of the moment and 3rd weeks of the varsity, the 1st week having been dedicated to introductory lectures. The paper via D. Cox is an outline of modern paintings in toric types and its purposes, placing into viewpoint the opposite contributions of the current volume.

Key phrases: Toric varieties

Class. math. : 14M25

Table of Contents

* D. A. Cox -- replace on toric geometry
* W. Bruns and J. Gubeladze -- Semigroup algebras and discrete geometry
* A. Craw and M. Reid -- tips to calculate A-Hilb C3
* D. I. Dais -- Resolving three-d toric singularities
* D. I. Dais -- Crepant resolutions of Gorenstein toric singularities and higher certain theorem
* J. Hausen -- generating stable quotients by means of embedding into toric varieties
* Y. Ito -- exact McKay correspondence
* Y. Tschinkel -- Lectures on top zeta capabilities of toric varieties
* J. A. Wiśniewski -- Toric Mori conception and Fano manifolds

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Soc. AG/980307. [30] V. -H. Saito, Y. Shimizu and K. Ueno, editors), World Sci. Publishing, River Edge, NJ, 1998, 1–32. A. COX [31] V. Batyrev and D. Cox, On the Hodge structure of projective hypersurfaces in toric varieties, Duke Math. J. 75 (1994), 293–338; alg-geom/9306011. [32] V. Batyrev and L. Borisov, Mirror duality and string-theoretic Hodge numbers, Invent. Math. 126 (1996), 183–203; alg-geom/9509009. [33] V. Batyrev and D. Dais, Strong McKay correspondence, string-theoretic Hodge numbers and mirror symmetry, Topology 35 (1996), 901–929; alg-geom/9410001.

44 3. Covering and normality . . . . . . . . . . . . . . . . . . . . 54 4. Divisorial linear algebra . . . . . . . . . . . . . . . . . . . . 70 5. From vector spaces to polytopal algebras . . . . . . . . . . . 88 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 1. Introduction These notes, composed for the Summer School on Toric Geometry at Grenoble, June/July 2000, contain a major part of the joint work of the authors.

125 1. Introduction These notes, composed for the Summer School on Toric Geometry at Grenoble, June/July 2000, contain a major part of the joint work of the authors. In Section 3 we study a problem that clearly belongs to the area of discrete geometry or, more precisely, to the combinatorics of finitely generated rational cones and their Hilbert bases. Our motivation in taking up this problem was the attempt 2000 Mathematics Subject Classification. — 13C14, 13C20, 13F20, 14M25, 20M25, 52B20.

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