Introduction à la géométrie tropicale
Ilia Itenberg1
1 IRMA, Université Louis Pasteur, 7, rue René Descartes, 67084 Strasbourg Cedex, France
Journées mathématiques X-UPS, Géométrie tropicale (2008), pp. 1-26.
DOI : 10.5802/xups.2008-01
Ilia Itenberg 1

1 IRMA, Université Louis Pasteur, 7, rue René Descartes, 67084 Strasbourg Cedex, France 
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Ilia Itenberg. Introduction à la géométrie tropicale. Journées mathématiques X-UPS, Géométrie tropicale (2008), pp. 1-26. doi : 10.5802/xups.2008-01. https://proceedings.centre-mersenne.org/articles/10.5802/xups.2008-01/

[1] G.M. Bergman The logarithmic limit-set of an algebraic variety, Trans. Amer. Math. Soc., Volume 157 (1971), pp. 459-469 | DOI | MR | Zbl

[2] D.N. Bernstein The number of roots of a system of equations, Funct. Anal. Appl., Volume 9 (1975) no. 3, pp. 183-185 | DOI | Zbl

[3] Herbert Busemann Convex surfaces, Interscience Tracts in Pure and Applied Math., 6, Interscience Publishers, Inc., New York, 1958 | MR

[4] Mikael Forsberg; Mikael Passare; August Tsikh Laurent determinants and arrangements of hyperplane amoebas, Adv. Math., Volume 151 (2000) no. 1, pp. 45-70 | DOI | MR | Zbl

[5] I.M. Gel’fand; M.M. Kapranov; A.V. Zelevinsky Discriminants, resultants, and multidimensional determinants, Mathematics : Theory & Appl., Birkhäuser Boston Inc., Boston, MA, 1994, x+523 pages | DOI | MR

[6] Ilia Itenberg Amibes de variétés algébriques et dénombrement de courbes (d’après G. Mikhalkin), Sém. Bourbaki (Vol. 2002/03) (Astérisque), Volume 294, Société Mathématique de France, Paris, 2004, pp. 335-361 (Exp. no 921) | MR | Zbl

[7] Ilia Itenberg; Viatcheslav Kharlamov; Eugenii Shustin Welschinger invariant and enumeration of real rational curves, Internat. Math. Res. Notices (2003) no. 49, pp. 2639-2653 | DOI | MR | Zbl

[8] Ilia Itenberg; Viatcheslav Kharlamov; Eugenii Shustin Logarithmic equivalence of the Welschinger and the Gromov-Witten invariants, Uspekhi Mat. Nauk, Volume 59 (2004) no. 6(360), pp. 85-110 (en russe). Trad. anglaise : arXiv: math.AG/0407188 | DOI | MR

[9] Ilia Itenberg; G. Mikhalkin; Eugenii Shustin Tropical algebraic geometry, Oberwolfach Seminars, 35, Birkhäuser Verlag, Basel, 2007 | MR

[10] M. Kapranov Amoebas over non-Archimedian fields (2000) (Prépublication)

[11] A Khovanskii; K. Kaveh Convex bodies and algebraic equations on affine varieties, 2008 | arXiv

[12] Maxim Kontsevich; Yan Soibelman Homological mirror symmetry and torus fibrations, Symplectic geometry and mirror symmetry (Seoul, 2000), World Sci. Publ., River Edge, NJ, 2001, pp. 203-263 | DOI | MR | Zbl

[13] G.L. Litvinov; V.P. Maslov The correspondence principle for idempotent calculus and some computer applications, Idempotency (Bristol, 1994) (Publ. Newton Inst.), Volume 11, Cambridge Univ. Press, Cambridge, 1998, pp. 420-443 | DOI | MR | Zbl

[14] G.L. Litvinov; V.P. Maslov; A.N. Sobolevskiĭ Idempotent mathematics and interval analysis, Vychisl. Tekhnol., Volume 6 (2001) no. 6, pp. 47-70 (arXiv :math.SC/9911126) | MR | Zbl

[15] G. Mikhalkin Real algebraic curves, the moment map and amoebas, Ann. of Math. (2), Volume 151 (2000) no. 1, pp. 309-326 | DOI | MR | Zbl

[16] G. Mikhalkin Counting curves via lattice paths in polygons, Comptes Rendus Mathématique, Volume 336 (2003) no. 8, pp. 629-634 | DOI | Numdam | MR | Zbl

[17] G. Mikhalkin Amoebas of algebraic varieties and tropical geometry, Different faces of geometry (Int. Math. Ser. (N. Y.)), Volume 3, Kluwer/Plenum, New York, 2004, pp. 257-300 | DOI | MR | Zbl

[18] G. Mikhalkin Decomposition into pairs-of-pants for complex algebraic hypersurfaces, Topology, Volume 43 (2004) no. 5, pp. 1035-1065 | DOI | MR | Zbl

[19] G. Mikhalkin Enumerative tropical algebraic geometry in ℝ 2 , J. Amer. Math. Soc., Volume 18 (2005) no. 2, pp. 313-377 | DOI | MR | Zbl

[20] G. Mikhalkin Tropical geometry and its applications, International Congress of Mathematicians. Vol. II, European Mathematical Society, Zürich, 2006, pp. 827-852 | MR | Zbl

[21] G. Mikhalkin; Hans Rullgård Amoebas of maximal area, Internat. Math. Res. Notices (2001) no. 9, pp. 441-451 | DOI | MR | Zbl

[22] Mikael Passare; Hans Rullgård Amoebas, Monge-Ampère measures, and triangulations of the Newton polytope, Duke Math. J., Volume 121 (2004) no. 3, pp. 481-507 | DOI | MR | Zbl

[23] Jean-Jacques Risler Construction d’hypersurfaces réelles (d’après Viro), Sem. Bourbaki (Vol. 1992/93) (Astérisque), Volume 216, Société Mathématique de France, Paris, 1993, pp. 69-86 (Exp. no 763) | Numdam | MR | Zbl

[24] L. Ronkin On zeros of almost periodic functions generated by functions holomorphic in a multicircular domain, Complex analysis in modern mathematics, FAZIS, Moscow, 2001, pp. 239-251 (en russe) | MR | Zbl

[25] Hans Rullgård Stratification des espaces de polynômes de Laurent et la structure de leurs amibes, C. R. Acad. Sci. Paris Sér. I Math., Volume 331 (2000) no. 5, pp. 355-358 | DOI | MR | Zbl

[26] Hans Rullgård Polynomial amoebas and convexity (2001) (Prépublication, Université de Stockholm)

[27] Bernd Sturmfels Solving systems of polynomial equations, CBMS Regional Conference Series in Math., 97, American Mathematical Society, Providence, RI, 2002 | DOI | MR

[28] Bernard Teissier Du théorème de l’index de Hodge aux inégalités isopérimétriques, C. R. Acad. Sci. Paris Sér. A-B, Volume 288 (1979) no. 4, p. A287-A289 | MR | Zbl

[29] O. Viro Gluing of algebraic hypersurfaces, smoothing of singularities and construction of curves, Proc. Leningrad Int. Topological Conf. (Leningrad, 1982), Nauka, Leningrad, 1983, pp. 149-197 (en russe)

[30] O. Viro Gluing of plane real algebraic curves and constructions of curves of degrees 6 and 7, Topology (Proceedings, Leningrad 1982) (Lect. Notes in Math.), Volume 1060, Springer, Berlin, 1984, pp. 187-200 | DOI | MR | Zbl

[31] O. Viro Dequantization of real algebraic geometry on logarithmic paper, European Congress of Mathematics, Vol. I (Barcelona, 2000) (Progress in Math.), Volume 201, Birkhäuser, Basel, 2001, pp. 135-146 | DOI | MR | Zbl

[32] R.J. Walker Algebraic curves, Princeton Math. Series, 13, Princeton University Press, Princeton, NJ, 1950 | MR

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