Comptes Rendus
Algebraic geometry/Differential geometry
Singularities and semistable degenerations for symplectic topology
Comptes Rendus. Mathématique, Volume 356 (2018) no. 4, pp. 420-432.

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.

Published online:
DOI: 10.1016/j.crma.2018.02.009

Mohammad F. Tehrani 1; Mark McLean 2; Aleksey Zinger 2

1 Simons Center for Geometry and Physics, Stony Brook University, Stony Brook, NY 11794, USA
2 Department of Mathematics, Stony Brook University, Stony Brook, NY 11794, USA
     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},
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%A Mark McLean
%A Aleksey Zinger
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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.

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