Comptes Rendus
no. 10
Symplectic capacities of toric manifolds and combinatorial inequalities
[Capacités symplectiques de variétés toriques et inéqualités combinatoires]
Guangcun Lu1
1 Department of Mathematics, Beijing Normal University, Beijing 100875, PR China
Comptes Rendus. Mathématique, Volume 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 :
Publié le :
DOI : 10.1016/S1631-073X(02)02357-9
Guangcun Lu 1

1 Department of Mathematics, Beijing Normal University, Beijing 100875, PR China 
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Guangcun Lu. Symplectic capacities of toric manifolds and combinatorial inequalities. Comptes Rendus. Mathématique, Volume 334 (2002) no. 10, pp. 889-892. doi : 10.1016/S1631-073X(02)02357-9. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02357-9/

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

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

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

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

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

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