Introduction à la géométrie tropicale
Itenberg, Ilia1
1 IRMA, Université Louis Pasteur, 7, rue René Descartes, 67084 Strasbourg Cedex, France
Journées mathématiques X-UPS, Géométrie tropicale (2008), pp. 1-26.
Publié le :
DOI : 10.5802/xups.2008-01
Itenberg, Ilia 1

1 IRMA, Université Louis Pasteur, 7, rue René Descartes, 67084 Strasbourg Cedex, France 
@incollection{XUPS_2008____1_0,
     author = {Itenberg, Ilia},
     title = {Introduction \`a~la~g\'eom\'etrie~tropicale},
     booktitle = {G\'eom\'etrie tropicale},
     series = {Journ\'ees math\'ematiques X-UPS},
     pages = {1--26},
     publisher = {Les \'Editions de l{\textquoteright}\'Ecole polytechnique},
     year = {2008},
     doi = {10.5802/xups.2008-01},
     language = {fr},
     url = {http://www.numdam.org/articles/10.5802/xups.2008-01/}
}
TY  - JOUR
AU  - Itenberg, Ilia
TI  - Introduction à la géométrie tropicale
JO  - Journées mathématiques X-UPS
PY  - 2008
SP  - 1
EP  - 26
PB  - Les Éditions de l’École polytechnique
UR  - http://www.numdam.org/articles/10.5802/xups.2008-01/
DO  - 10.5802/xups.2008-01
LA  - fr
ID  - XUPS_2008____1_0
ER  - 
%0 Journal Article
%A Itenberg, Ilia
%T Introduction à la géométrie tropicale
%J Journées mathématiques X-UPS
%D 2008
%P 1-26
%I Les Éditions de l’École polytechnique
%U http://www.numdam.org/articles/10.5802/xups.2008-01/
%R 10.5802/xups.2008-01
%G fr
%F XUPS_2008____1_0
Itenberg, Ilia. Introduction à la géométrie tropicale. Journées mathématiques X-UPS, Géométrie tropicale (2008), pp. 1-26. doi : 10.5802/xups.2008-01. http://www.numdam.org/articles/10.5802/xups.2008-01/

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[22] Passare, Mikael; Rullgård, Hans 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] Risler, Jean-Jacques 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] Ronkin, L. 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] Rullgård, Hans 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] Rullgård, Hans Polynomial amoebas and convexity (2001) (Prépublication, Université de Stockholm)

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

[28] Teissier, Bernard 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] Viro, O. 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] Viro, O. 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] Viro, O. 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] Walker, R.J. Algebraic curves, Princeton Math. Series, 13, Princeton University Press, Princeton, NJ, 1950 | MR

Cité par Sources :