Singularities and semistable degenerations for symplectic topology

Mohammad F. Tehrani; Mark McLean; Aleksey Zinger

doi:10.1016/j.crma.2018.02.009

Singularities and semistable degenerations for symplectic topology

Mohammad F. Tehrani
, Mark McLean
, Aleksey Zinger

Mathematics

Stony Brook University

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	420-432
Number of pages	13
Journal	Comptes Rendus Mathematique
Volume	356
Issue number	4
DOIs	https://doi.org/10.1016/j.crma.2018.02.009
State	Published - Apr 2018

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title = "Singularities and semistable degenerations for symplectic topology",

abstract = "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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AU - McLean, Mark

AU - Zinger, Aleksey

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N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/85042360901

U2 - 10.1016/j.crma.2018.02.009

DO - 10.1016/j.crma.2018.02.009

M3 - Article

AN - SCOPUS:85042360901

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JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

IS - 4

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Singularities and semistable degenerations for symplectic topology

Abstract

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