Invariants de Welschinger

Oancea, Alexandru

Séminaire Bourbaki Volume 2010/2011 Exposés 1027-1042. Avec table par noms d'auteurs de 1948/49 à 2009/10., Astérisque, no. 348 (2012), Exposé no. 1036, 33 p.

Zbl

@incollection{AST_2012__348__265_0,
     author = {Oancea, Alexandru},
     title = {Invariants de {Welschinger}},
     booktitle = {S\'eminaire Bourbaki Volume 2010/2011 Expos\'es 1027-1042. Avec table par noms d'auteurs de 1948/49 \`a 2009/10.},
     series = {Ast\'erisque},
     note = {talk:1036},
     pages = {265--297},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {348},
     year = {2012},
     zbl = {1279.53081},
     language = {fr},
     url = {http://archive.numdam.org/item/AST_2012__348__265_0/}
}

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Oancea, Alexandru. Invariants de Welschinger, dans Séminaire Bourbaki Volume 2010/2011 Exposés 1027-1042. Avec table par noms d'auteurs de 1948/49 à 2009/10., Astérisque, no. 348 (2012), Exposé no. 1036, 33 p. http://archive.numdam.org/item/AST_2012__348__265_0/

Bibliographie
Cité par

[1] A. Arroyo, E. Brugallé & L. López De Medrano - Recursive formulas for Welschinger invariants of the projective plane, Int. Math. Res. Not. 2011 (2011), p. 1107-1134. | Zbl

[2] J.-F. Barraud - Nodal symplectic spheres in $𝐂 P^{2}$ with positive self-intersection, Int. Math. Res. Not. 1999 (1999), p. 495-508. | DOI | Zbl

[3] F. Bourgeois - A Morse-Bott approach to contact homology, These, Stanford University, 2002. | Zbl

[4] F. Bourgeois, Y. Eliashberg, H. Hofer, K. Wysocki & E. Zehnder - Compactness results in symplectic field theory, Geom. Topol. 7 (2003), p. 799-888. | DOI | EuDML | Zbl

[5] E. Brugallé & G. Mikhalkin - Enumeration of curves via floor diagrams, C. R. Math. Acad. Sci. Paris 345 (2007), p. 329-334. | DOI | Zbl

[6] L. Caporaso & J. Harris - Counting plane curves of any genus, Invent. Math. 131 (1998), p. 345-392. | DOI | Zbl

[7] C.-H. Cho - Counting real $J$ -holomorphic discs and spheres in dimension four and six, J. Korean Math. Soc. 45 (2008), p. 1427-1442. | DOI | Zbl

[8] A. I. Degtyarev & V. Kharlamov - Topological properties of real algebraic varieties : Rokhlin's way, Uspekhi Mat. Nauk 55 (2000), p. 129-212 (in Russian) | Zbl

A. I. Degtyarev & V. Kharlamov - Topological properties of real algebraic varieties : Rokhlin's way, English translation : Russian Math. Surveys 55 (2000), p. 735-814. | DOI | Zbl

[9] Y. Eliashberg, A. Givental & H. Hofer - Introduction to symplectic field theory, Geom. Fund. Anal. Special Volume, Part II (2000), p. 560-673. | Zbl

[10] K. Fukaya - Counting pseudo-holomorphic discs in Calabi-Yau 3-fold, prepublication arXiv:0908.0148. | Zbl

[11] K. Fukaya, Y.-G. Oh, H. Ohta & K. Ono - Lagrangian intersection Floer theory : anomaly and obstruction, AMS/IP Studies in Adv. Math., vol. 46. 1-2, AMS-International Press, 2009. | Zbl

[12] K. Fukaya, Y.-G. Oh, H. Ohta & K. Ono, Anti-symplectic involution and Floer cohomology, prepublication arXiv:0912.2646.

[13] W. Fulton & R. Pandharipande - Notes on stable maps and quantum cohomology, in Algebraic geometry - Santa Cruz 1995, Proc. Sympos. Pure Math., vol. 62, Amer. Math. Soc., 1997, p. 45-96. | DOI | Zbl

[14] A. Gathmann & H. Markwig - The Caporaso-Harris formula and plane relative Gromov-Witten invariants in tropical geometry, Math. Ann. 338 (2007), p. 845-868. | DOI | Zbl

[15] A. Gathmann, H. Markwig & F. Schroeter - Broccoli curves and the tropical invariance of Welschinger numbers, prépublication arXiv:1104.3118. | DOI | Zbl

[16] M. Gromov - Pseudoholomorphic curves in symplectic manifolds, Invent. Math. 82 (1985), p. 307-347. | DOI | EuDML | Zbl

[17] H. Hofer - Pseudoholomorphic curves in symplectizations with applications to the Weinstein conjecture in dimension three, Invent. Math. 114 (1993), p. 515-563. | DOI | EuDML | Zbl

[18] H. Hofer, K. Wysocki & E. Zehnder - Properties of pseudo-holomorphic curves in symplectizations. II. Embedding controls and algebraic invariants, Geom. Fund. Anal. 5 (1995), p. 270-328. | DOI | EuDML | Zbl

[19] H. Hofer, K. Wysocki & E. Zehnder, Properties of pseudoholomorphic curves in symplectizations. I. Asymptotics, Ann. Inst. H. Poincaré Anal. Non Linéaire 13 (1996), p. 337-379. | DOI | EuDML | Numdam | Zbl

[20] H. Hofer, K. Wysocki & E. Zehnder, Properties of pseudoholomorphic curves in symplectizations. III. Fredholm theory, in Topics in nonlinear analysis, Progr. Nonlinear Differential Equations Appl, vol. 35, Birkhäuser, 1999, p. 381-475. | DOI | Zbl

[21] H. Hofer, K. Wysocki & E. Zehnder, A general Fredholm theory. II. Implicit function theorems, Geom. Funct. Anal. 19 (2009), p. 206-293. | DOI | Zbl

[22] E.-N. Ionel & T. H. Parker - The symplectic sum formula for Gromov-Witten invariants, Ann. of Math. 159 (2004), p. 935-1025. | DOI | Zbl

[23] I. Itenberg - Amibes de variétés algébriques et dénombrement de courbes (d'après G. Mikhalkin), Séminaire Bourbaki, vol. 2002/03, exp. n° 921, Astérisque 294 (2004), p. 335-361. | EuDML | Numdam | Zbl

[24] I. Itenberg, V. Kharlamov & E. Shustin - Welschinger invariant and enumeration of real rational curves, Int. Math. Res. Not. 2003 (2003), p. 2639-2653. | DOI | Zbl

[25] I. Itenberg, V. Kharlamov & E. Shustin, Logarithmic equivalence of the Welschinger and the Gromov-Witten invariants, Uspekhi Mat. Nauk 59 (2004), p. 85-110 (in Russian) | Zbl

I. Itenberg, V. Kharlamov & E. Shustin, Logarithmic equivalence of the Welschinger and the Gromov-Witten invariants ; English translation : Russian Math. Surveys 59 (2004), 1093-1116. | DOI | Zbl

[26] I. Itenberg, V. Kharlamov & E. Shustin, A Caporaso-Harris type formula for Welschinger invariants of real toric del Pezzo surfaces, Comment. Math. Helv. 84 (2009), p. 87-126. | DOI | Zbl

[27] I. Itenberg, G. Mikhalkin & E. Shustin - Tropical algebraic geometry, second ed., Oberwolfach Seminars, vol. 35, Birkhäuser, 2009. | Zbl

[28] S. Ivashkovich & V. Shevchishin - Structure of the moduli space in a neighborhood of a cusp-curve and meromorphic hulls, Invent. Math. 136 (1999), p. 571-602. | DOI | Zbl

[29] V. Kharlamov - Variétés de Fano réelles (d'après C. Viterbo), Séminaire Bourbaki, vol. 1999/2000, exp. n° 872, Astérisque 276 (2002), p. 189-206. | EuDML | Numdam | Zbl

[30] R. C. Kirby & L. R. Taylor - Pin structures on low-dimensional manifolds, in Geometry of low-dimensional manifolds, 2 (Durham, 1989), London Math. Soc. Lecture Note Ser., vol. 151, Cambridge Univ. Press, 1990, p. 177-242. | Zbl

[31] S. Kobayashi - Differential geometry of complex vector bundles, Publications of the Mathematical Society of Japan, vol. 15, Princeton Univ. Press, 1987. | MR | Zbl

[32] M. Kontsevich - Homological algebra of mirror symmetry, in Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Zurich, 1994), Birkhäuser, 1995, p. 120-139. | DOI | MR | Zbl

[33] M. Kontsevich & Y. Manin - Gromov-Witten classes, quantum cohomology, and enumerative geometry, Comm. Math. Phys. 164 (1994), p. 525-562. | DOI | MR | Zbl

[34] F. Mangolte & J.-Y. Welschinger - Do uniruled six-manifolds contain Sol Lagrangian submanifolds ?, prépublication arXiv:1001.2927. | DOI | MR | Zbl

[35] D. Mcduff & D. Salamon - $J$ -holomorphic curves and symplectic topology, American Mathematical Society Colloquium Publications, vol. 52, Amer. Math. Soc, 2004. | MR | Zbl

[36] G. Mikhalkin - Enumerative tropical algebraic geometry in $ℝ^{2}$ , J. Amer. Math. Soc. 18 (2005), p. 313-377. | DOI | MR | Zbl

[37] J. W. Milnor & J. D. Stasheff - Characteristic classes, Annals of Math. Studies, vol. 76, Princeton Univ. Press, 1974. | MR | Zbl

[38] R. Pandharipande, J. P. Solomon & J. Walcher - Disk enumeration on the quintic 3-fold, J. Amer. Math. Soc. 21 (2008), p. 1169-1209. | DOI | MR | Zbl

[39] F. Ronga, A. Tognoli & T. Vust - The number of conics tangent to five given conics : the real case, Rev. Mat. Univ. Complut. Madrid 10 (1997), p. 391-421. | EuDML | MR | Zbl

[40] Y. Ruan & G. Tian - A mathematical theory of quantum cohomology, J. Differential Geom. 42 (1995), p. 259-367. | DOI | MR | Zbl

[41] V. Schevchishin - Pseudoholomorphic curves and the symplectic isotopy problem, Habilitationsschrift, Universität Bochum-Ruhr, 2000, arXiv:math/0010262.

[42] E. Shustin - A tropical calculation of the Welschinger invariants of real toric del Pezzo surfaces, J. Algebraic Geom. 15 (2006), p. 285-322. | DOI | MR | Zbl

[43] J. P. Solomon - Intersection theory on the moduli space of holomorphic curves with Lagrangian boundary conditions, Thèse, Massachusetts Institute of Technology, 2006, arXiv:math/0606429. | MR

[44] F. Sottile - Enumerative real algebraic geometry, in Algorithmic and quantitative real algebraic geometry (Piscataway, NJ, 2001), DIMACS Ser. Discrete Math. Theoret. Comput. Ser., vol. 60, Amer. Math. Soc, 2003, p. 139-179. | DOI | MR | Zbl

[45] C. Viterbo - A new obstruction to embedding Lagrangian tori, Invent. Math. 100 (1990), p. 301-320. | DOI | EuDML | MR | Zbl

[46] C. Viterbo, Symplectic real algebraic geometry, 1999.

[47] A. Weinstein - Symplectic manifolds and their Lagrangian submanifolds, Advances in Math. 6 (1971), p. 329-346. | DOI | MR | Zbl

[48] J.-Y. Welschinger - Invariants of real rational symplectic 4-manifolds and lower bounds in real enumerative geometry, C. R. Math. Acad. Sci. Paris 336 (2003), p. 341-344. | DOI | MR | Zbl

[49] J.-Y. Welschinger, Invariants of real symplectic 4-manifolds and lower bounds in real enumerative geometry, Invent. Math. 162 (2005), p. 195-234. | DOI | MR | Zbl

[50] J.-Y. Welschinger, Spinor states of real rational curves in real algebraic convex 3-manifolds and enumerative invariants, Duke Math. J. 127 (2005), p. 89-121. | DOI | MR | Zbl

[51] J.-Y. Welschinger, Invariants of real symplectic four-manifolds out of reducible and cuspidal curves, Bull. Soc. Math. France 134 (2006), p. 287-325. | DOI | EuDML | Numdam | MR | Zbl

[52] J.-Y. Welschinger, Towards relative invariants of real symplectic four-manifolds, Geom. Fund. Anal. 16 (2006), p. 1157-1182. | DOI | MR | Zbl

[53] J.-Y. Welschinger, Invariant count of holomorphic disks in the cotangent bundles of the two-sphere and real projective plane, C. R. Math. Acad. Sci. Paris 344 (2007), p. 313-316. | DOI | MR | Zbl

[54] J.-Y. Welschinger, Invariants entiers en géométrie enumerative réelle, in Proceedings of the International Congress of Mathematicians. Volume II, Hindustan Book Agency, 2010, p. 652-678. | MR | Zbl

[55] J.-Y. Welschinger, Enumerative invariants of strongly semipositive real symplectic six-manifolds, prépublication arXiv: math/0509121.

[56] J.-Y. Welschinger, Open Gromov-Witten invariants in dimension four, prépublication arXiv:1110.2705. | DOI | MR | Zbl

[57] J.-Y. Welschinger, Open Gromov-Witten invariants in dimension six, prépublication arXiv:1201.3518. | DOI | MR | Zbl

[58] J.-Y. Welschinger, Open strings, Lagrangian conductors and Floer functor, prépublication arXiv:0812.0276.

[59] J.-Y. Welschinger, Optimalité, congruences et calculs d'invariants des variétés symplectiques réelles de dimension quatre, prépublication arXiv:0707.4317.