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.
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.
Accepted:
Published online:
Mohammad F. Tehrani 1; Mark McLean 2; Aleksey Zinger 2
@article{CRMATH_2018__356_4_420_0,
author = {Mohammad F. Tehrani and Mark McLean and Aleksey Zinger},
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},
}
TY - JOUR AU - Mohammad F. Tehrani AU - Mark McLean AU - Aleksey Zinger TI - Singularities and semistable degenerations for symplectic topology JO - Comptes Rendus. Mathématique PY - 2018 SP - 420 EP - 432 VL - 356 IS - 4 PB - Elsevier DO - 10.1016/j.crma.2018.02.009 LA - en ID - CRMATH_2018__356_4_420_0 ER -
Mohammad F. Tehrani; Mark McLean; Aleksey Zinger. Singularities and semistable degenerations for symplectic topology. Comptes Rendus. Mathématique, Volume 356 (2018) no. 4, pp. 420-432. doi : 10.1016/j.crma.2018.02.009. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2018.02.009/
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