[Invariants des variétés symplectiques rationnelles réelles de dimension quatre, et bornes inférieures en géométrie énumérative réelle]
Suivant l'approche de Gromov et Witten, nous construisons des invariants par déformation des variétés symplectiques réelles rationnelles de dimension quatre. Ces invariants fournissent des bornes inférieures pour le nombre de courbes J-holomorphes rationnelles réelles de classe d'homologie donnée passant par une configuration réelle de points donnée.
Following the approach of Gromov and Witten, we construct invariants under deformation of real rational symplectic 4-manifolds. These invariants provide lower bounds for the number of real rational J-holomorphic curves in a given homology class passing through a given real configuration of points.
Accepté le :
Publié le :
@article{CRMATH_2003__336_4_341_0,
author = {Welschinger, Jean-Yves},
title = {Invariants of real rational symplectic 4-manifolds and lower bounds in real enumerative geometry},
journal = {Comptes Rendus. Math\'ematique},
pages = {341--344},
publisher = {Elsevier},
volume = {336},
number = {4},
year = {2003},
doi = {10.1016/S1631-073X(03)00059-1},
language = {en},
url = {http://archive.numdam.org/articles/10.1016/S1631-073X(03)00059-1/}
}
TY - JOUR AU - Welschinger, Jean-Yves TI - Invariants of real rational symplectic 4-manifolds and lower bounds in real enumerative geometry JO - Comptes Rendus. Mathématique PY - 2003 SP - 341 EP - 344 VL - 336 IS - 4 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/S1631-073X(03)00059-1/ DO - 10.1016/S1631-073X(03)00059-1 LA - en ID - CRMATH_2003__336_4_341_0 ER -
%0 Journal Article %A Welschinger, Jean-Yves %T Invariants of real rational symplectic 4-manifolds and lower bounds in real enumerative geometry %J Comptes Rendus. Mathématique %D 2003 %P 341-344 %V 336 %N 4 %I Elsevier %U http://archive.numdam.org/articles/10.1016/S1631-073X(03)00059-1/ %R 10.1016/S1631-073X(03)00059-1 %G en %F CRMATH_2003__336_4_341_0
Welschinger, Jean-Yves. Invariants of real rational symplectic 4-manifolds and lower bounds in real enumerative geometry. Comptes Rendus. Mathématique, Tome 336 (2003) no. 4, pp. 341-344. doi : 10.1016/S1631-073X(03)00059-1. http://archive.numdam.org/articles/10.1016/S1631-073X(03)00059-1/
[1] Topological properties of real algebraic varieties: Rokhlin's way, Uspekhi Mat. Nauk, Volume 55 (2000), pp. 129-212
[2] On genericity for holomorphic curves in four-dimensional almost-complex manifolds, J. Geom. Anal., Volume 7 (1997), pp. 149-159
[3] Structure of the moduli space in a neighborhood of a cusp-curve and meromorphic hulls, Invent. Math., Volume 136 (1999), pp. 571-602
[4] Gromov–Witten classes, quantum cohomology, and enumerative geometry, Comm. Math. Phys., Volume 164 (1994), pp. 525-562
[5] A survey of symplectic 4-manifolds with b+=1, Turkish J. Math., Volume 20 (1996), pp. 47-60
[6] V.V. Shevchishin, Pseudoholomorphic curves and the symplectic isotopy problem, Preprint , 2000 | arXiv
[7] F. Sottile, Enumerative real algebraic geometry, electronic survey at http://www.maths.univ-rennes1.fr/~raag01/surveys/ERAG/index.html, 2002
Cité par Sources :
