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.

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Published online:
DOI: 10.1016/j.crma.2018.02.009
Tehrani, Mohammad F. 1; McLean, Mark 2; Zinger, Aleksey 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
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Tehrani, Mohammad F.; McLean, Mark; Zinger, Aleksey. 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. http://www.numdam.org/articles/10.1016/j.crma.2018.02.009/

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