[Singularités et dégénérescences semi-stables en topologie symplectique]
Nous résumons nos travaux [7–11,6], où l'on définit et étudie les variétés et sous-variétés à croisements normaux en géométrie symplectique. Ils répondent à une question de Gromov sur la possibilité d'introduire de telles (sous-)variétés singuliéres en topologie symplectique, dans le cas de singularités à croisements normaux. Nous donnons également une condition nécessaire et suffisante pour lisser ces variétés symplectiques à croisements normaux. De plus, nous expliquons les liens avec d'autres domaines mathématiques et discutons quelques directions pour de futures recherches.
We overview our work [7–11,6] defining and studying normal crossings varieties and subvarieties in symplectic topology. This work answers a question of Gromov on the feasibility of introducing singular (sub)varieties into symplectic topology in the case of normal crossings singularities. It also provides a necessary and sufficient condition for smoothing normal crossings symplectic varieties. In addition, we explain some connections with other areas of mathematics and discuss a few directions for further research.
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@article{CRMATH_2018__356_4_420_0,
author = {Tehrani, Mohammad F. and McLean, Mark and Zinger, Aleksey},
title = {Singularities and semistable degenerations for symplectic topology},
journal = {Comptes Rendus. Math\'ematique},
pages = {420--432},
publisher = {Elsevier},
volume = {356},
number = {4},
year = {2018},
doi = {10.1016/j.crma.2018.02.009},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2018.02.009/}
}
TY - JOUR AU - Tehrani, Mohammad F. AU - McLean, Mark AU - Zinger, Aleksey TI - Singularities and semistable degenerations for symplectic topology JO - Comptes Rendus. Mathématique PY - 2018 SP - 420 EP - 432 VL - 356 IS - 4 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2018.02.009/ DO - 10.1016/j.crma.2018.02.009 LA - en ID - CRMATH_2018__356_4_420_0 ER -
%0 Journal Article %A Tehrani, Mohammad F. %A McLean, Mark %A Zinger, Aleksey %T Singularities and semistable degenerations for symplectic topology %J Comptes Rendus. Mathématique %D 2018 %P 420-432 %V 356 %N 4 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2018.02.009/ %R 10.1016/j.crma.2018.02.009 %G en %F CRMATH_2018__356_4_420_0
Tehrani, Mohammad F.; McLean, Mark; Zinger, Aleksey. Singularities and semistable degenerations for symplectic topology. Comptes Rendus. Mathématique, Tome 356 (2018) no. 4, pp. 420-432. doi : 10.1016/j.crma.2018.02.009. http://www.numdam.org/articles/10.1016/j.crma.2018.02.009/
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