Geodesic
Holomorphic 2-Forms and Vanishing Theorems for Gromov–Witten Invariants
Canadian mathematical bulletin, Tome 52 (2009) no. 1, pp. 87-94

Voir la notice de l'article provenant de la source Cambridge University Press

On a compact Kähler manifold $X$ with a holomorphic 2-form $\alpha$ , there is an almost complex structure associated with α. We show how this implies vanishing theorems for the Gromov–Witten invariants of $X$ . This extends the approach used by Parker and the author for Kähler surfaces to higher dimensions.
DOI : 10.4153/CMB-2009-011-1
Mots-clés : 53D45 
Lee, Junho. Holomorphic 2-Forms and Vanishing Theorems for Gromov–Witten Invariants. Canadian mathematical bulletin, Tome 52 (2009) no. 1, pp. 87-94. doi: 10.4153/CMB-2009-011-1
@article{10_4153_CMB_2009_011_1,
     author = {Lee, Junho},
     title = {Holomorphic {2-Forms} and {Vanishing} {Theorems} for {Gromov{\textendash}Witten} {Invariants}},
     journal = {Canadian mathematical bulletin},
     pages = {87--94},
     year = {2009},
     volume = {52},
     number = {1},
     doi = {10.4153/CMB-2009-011-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2009-011-1/}
}
TY  - JOUR
AU  - Lee, Junho
TI  - Holomorphic 2-Forms and Vanishing Theorems for Gromov–Witten Invariants
JO  - Canadian mathematical bulletin
PY  - 2009
SP  - 87
EP  - 94
VL  - 52
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2009-011-1/
DO  - 10.4153/CMB-2009-011-1
ID  - 10_4153_CMB_2009_011_1
ER  - 
%0 Journal Article
%A Lee, Junho
%T Holomorphic 2-Forms and Vanishing Theorems for Gromov–Witten Invariants
%J Canadian mathematical bulletin
%D 2009
%P 87-94
%V 52
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2009-011-1/
%R 10.4153/CMB-2009-011-1
%F 10_4153_CMB_2009_011_1

[B] Behrend, K., The product formula for Gromov–Witten invariants. J. Algebraic Geom. 8(1999), no. 3, 529–541. Google Scholar

[BDL] Bryan, J., Donagi, R., and Leung, N. C., G-bundles on abelian surfaces, hyperkähler manifolds, and stringy Hodge numbers. Turkish J. Math. 25(2001), no. 1, 195–236. Google Scholar

[BHPV] Barth, W., Hulek, K., Peters, C., and de Ven, A. Van, Compact complex surfaces, Second ed., Springer-Verlag, Berlin, 2004. Google Scholar

[BL] Bryan, J. and Leung, N. C., Counting curves on irrational surfaces. In: Surveys in differential geometry: differential geometry inspired by string theory, Surv. Diff. Geom., 5, Int. Press, Boston, MA, 1999, pp. 313–339. Google Scholar

[CN] Camacho, C. and Neto, A. L., Geometric theory of foliations. Birkhäuser Boston, Inc., Boston, MA, 1985. Google Scholar

[CP] Campana, F. and Peternell, T., Complex threefolds with non-trivial holomorphic 2-forms. J. Algebraic Geom. 9(2000), no. 2, 223–264. Google Scholar

[H] Höring, A., Uniruled varieties with split tangent bundle. Math. Z. 256(2007), no. 3, 465–479. Google Scholar

[Ho] Holmann, H., On the stability of holomorphic foliations, Analytic functions, Kozubnik 1979, Lecture Notes in Math. 798, Springer, Berlin, 1980. pp. 192–202. Google Scholar

[HZ] Hori, K., Katz, S., Klemm, A., Pandharipande, R., Thomas, R., Vafa, C., Vakil, R., and Zaslow, E., Mirror symmetry, Clay Mathematics Monographs 1. American Mathematical Society, Providence, RI, Clay Mathematics Institute, Cambridge, MA, 2003. Google Scholar

[L] Lee, J., Family Gromov–Witten Invariants for Kähler Surfaces. Duke Math. J. 123(2004), no. 1, 209–233. Google Scholar

[LP] Lee, J. and Parker, T. H., A structure theorem for the Gromov–Witten invariants of Kähler surfaces. J. Differential Geom. 77(2007), no. 3, 483–513. Google Scholar

[Le] Lehmann, D., Résidues des sous-variétés invariantes d’un feuilletage singulier. Ann. Inst. Fourier 41(1991), no. 1, 211–258. Google Scholar

[LT] Li, J. and Tian, G., Virtual moduli cycles and Gromov–Witten invariants of general symplectic manifolds. Topics in symplectic 4-manifolds, First Int. Press Lect. Ser. I, International Press, Cambridge, MA, 1998, pp. 47–83. Google Scholar

Cité par Sources :