Rationally connected $3$-folds and symplectic geometry

Rationally connected

3

-folds and symplectic geometry

Voisin, Claire

Géométrie différentielle, physique mathématique, mathématiques et société (II) - Volume en l'honneur de Jean-Pierre Bourguignon, Astérisque, no. 322 (2008), p. 1-21

MR 2521651 | Zbl 1178.14048

@incollection{AST_2008__322__1_0,
     author = {Voisin, Claire},
     title = {Rationally connected $3$-folds and symplectic geometry},
     booktitle = {G\'eom\'etrie diff\'erentielle, physique math\'ematique, math\'ematiques et soci\'et\'e (II) - Volume en l'honneur de Jean-Pierre Bourguignon},
     editor = {Hijazi Oussama},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {322},
     year = {2008},
     pages = {1-21},
     zbl = {1178.14048},
     mrnumber = {2521651},
     language = {en},
     url = {http://www.numdam.org/item/AST_2008__322__1_0}
}

Voisin, Claire. Rationally connected $3$-folds and symplectic geometry, in Géométrie différentielle, physique mathématique, mathématiques et société (II) - Volume en l'honneur de Jean-Pierre Bourguignon, Astérisque, no. 322 (2008), pp. 1-21. http://www.numdam.org/item/AST_2008__322__1_0/

References

[1] K. Behrend & B. Fantechi - "The intrinsic normal cone", Invent. Math. 128 (1997), p. 45-88. | Article | MR 1437495 | Zbl 0909.14006

[2] F. Campana - "Connexité rationnelle des variétés de Fano", Ann. Sci. École Norm. Sup. 25 (1992), p. 539-545. | Article | Numdam | MR 1191735 | Zbl 0783.14022

[3] F. Campana & T. Peternell - "Rigidity theorems for primitive Fano $3$ -folds", Comm. Anal. Geom. 2 (1994), p. 173-201. | Article | MR 1312685 | Zbl 0864.14024

[4] 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. | Article | MR 1492534 | Zbl 0898.14018

[5] T. Graber, J. Harris & J. Starr - "Families of rationally connected varieties", J. Amer. Math. Soc. 16 (2003), p. 57-67. | Article | MR 1937199 | Zbl 1092.14063

[6] J. Hu, T.-J. Li & Y. Ruan - "Birational cobordism invariance of uniruled symplectic manifolds", Invent. Math. 172 (2008), p. 231-275. | Article | MR 2390285 | Zbl 1163.53055

[7] Y. Kawamata, K. Matsuda & K. Matsuki - "Introduction to the minimal model problem", in Algebraic geometry, Sendai, 1985, Adv. Stud. Pure Math., vol. 10, North-Holland, 1987, p. 283-360. | Article | MR 946243 | Zbl 0672.14006

[8] J. Kollár - Rational curves on algebraic varieties, Ergebnisse der Mathematik und ihrer Grenzgebiete, vol. 32, Springer, 1996. | MR 1440180 | Zbl 0877.14012

[9] J. Kollár, "Low degree polynomial equations: arithmetic, geometry and topology", in European Congress of Mathematics, Vol. I (Budapest, 1996), Progr. Math., vol. 168, Birkhäuser, 1998, p. 255-288. | MR 1645812 | Zbl 0970.14001

[10] J. Kollár, Y. Miyaoka & S. Mori - "Rational connectedness and boundedness of Fano manifolds", J. Differential Geom. 36 (1992), p. 765-779. | Article | MR 1189503 | Zbl 0759.14032

[11] J. Kollár, Y. Miyaoka & S. Mori, "Rationally connected varieties", J. Algebraic Geom. 1 (1992), p. 429-448. | MR 1158625 | Zbl 0780.14026

[12] J. Li & G. Tian - "Comparison of algebraic and symplectic Gromov-Witten invariants", Asian J. Math. 3 (1999), p. 689-728. | Article | MR 1793677 | Zbl 0983.53061

[13] D. Mcduff - "The structure of rational and ruled symplectic $4$ -manifolds", J. Amer. Math. Soc. 3 (1990), p. 679-712. | MR 1049697 | Zbl 0723.53019

[14] D. Mcduff, "Hamiltonian $S^{1}$ manifolds are uniruled", preprint, 2007. | MR 2484280 | Zbl 1183.53080

[15] Y. Miyaoka & T. Peternell - Geometry of higher-dimensional algebraic varieties, DMV Seminar, vol. 26, Birkhäuser, 1997. | MR 1468476 | Zbl 0865.14018

[16] S. Mori - "Threefolds whose canonical bundles are not numerically effective", Ann. of Math. 116 (1982), p. 133-176. | Article | MR 662120 | Zbl 0557.14021

[17] S. Mori & S. Mukai - "Classification of Fano $3$ -folds with $B_{2} \geq 2$ ", Manuscripta Math. 36 (1981/82), p. 147-162. | Article | MR 641971 | Zbl 0478.14033

[18] Y. Ruan - "Symplectic topology and extremal rays", Geom. Funct. Anal. 3 (1993), p. 395-430. | Article | MR 1223437 | Zbl 0806.53032

[19] Y. Ruan, "Virtual neighborhoods and pseudo-holomorphic curves", in Proceedings of 6th Gökova Geometry-Topology Conference, vol. 23, 1999, p. 161-231. | MR 1701645 | Zbl 0967.53055

[20] B. Siebert - "Algebraic and symplectic Gromov-Witten invariants coincide", Ann. Inst. Fourier (Grenoble) 49 (1999), p. 1743-1795. | Article | Numdam | MR 1738065 | Zbl 0970.14030