Symplectic capacities of toric manifolds and combinatorial inequalities
[Capacités symplectiques de variétés toriques et inéqualités combinatoires]
Lu, Guangcun1
1 Department of Mathematics, Beijing Normal University, Beijing 100875, PR China
Comptes Rendus. Mathématique, Tome 334 (2002) no. 10, pp. 889-892.
est référencé par Corrigendum to the Note “Symplectic capacities of toric manifolds and combinatorial inequalities” [C. R. Acad. Sci. Paris, Ser. I 334 (10) (2002) 889–892]
[Capacités symplectiques de variétés toriques et des associés résultats]

On obtient des estimations concrètes pour le largeur symplectique de Gromov pour les variétés toriques par ses données combinatoires. Comme un sous-produit, quelques inéqualités combinatoires dans la théorie de polytope sont obtenus.

We shall give concrete estimations for the Gromov symplectic width of toric manifolds in combinatorial data. As by-products some combinatorial inequalities in the polytope theory are obtained.

Reçu le :
Accepté le :
DOI : 10.1016/S1631-073X(02)02357-9
Lu, Guangcun 1

1 Department of Mathematics, Beijing Normal University, Beijing 100875, PR China 
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Lu, Guangcun. Symplectic capacities of toric manifolds and combinatorial inequalities. Comptes Rendus. Mathématique, Tome 334 (2002) no. 10, pp. 889-892. doi : 10.1016/S1631-073X(02)02357-9. http://www.numdam.org/articles/10.1016/S1631-073X(02)02357-9/

[1] Audin, M. The Topology of Torus Actions on Symplectic Manifolds, Progress in Math., 93, Birkhäuser, 1991

[2] Batyrev, V.V. Quantum cohomology rings of toric manifolds, Astérisque, Volume 218 (1993), pp. 9-34

[3] Biran, P.; Cieliebak, K. Symplectic topology on subcritical manifolds, Comment. Math. Helv., Volume 76 (2001), pp. 712-753

[4] Demailly, J.-P. L2-vanishing theorems for positive line bundles and adjunction theory (Catanese, F.; Ciliberto, C., eds.), Transcendental Methods in Algebraic Geometry, Lecture Notes Math., 1646, Springer-Verlag, 1992, pp. 1-97

[5] Guillemin, V. Moment maps and combinatorial invariants of Hamiltonian 𝕋 n -spaces, Progress in Math., 122, Birkhäuser, 1994

[6] G.C. Lu, Gromov–Witten invariants and pseudo symplectic capacities, Preprint, math.SG/0103195, v6, 6 September, 2001

[7] F. Schlenk, On symplectic folding, Preprint, math.SG/9903086, March 1999

[8] Siebert, B. An update on (small) quantum cohomology (Phong, D.H.; Vinet, L.; Yau, S.T., eds.), Mirror Symmetry III, International Press, 1999, pp. 279-312

[9] Sikorav, J.C. Rigidité symplectique dans le cotangent de 𝕋 n , Duke Math. J., Volume 59 (1989), pp. 227-231

[10] Viterbo, C. Metric and isoperimetric problems in symplectic geometry, J. Amer. Math. Soc., Volume 13 (2000), pp. 411-431

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