Symplectic conifold transitions

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dc.creatorSmith, I.
dc.creatorThomas, R. P.
dc.creatorYau, S. -T.
dc.date2002-09-24
dc.date2003-05-22
dc.date.accessioned2026-07-07T06:33:33Z
dc.date.available2026-07-07T06:33:33Z
dc.descriptionWe introduce a symplectic surgery in six dimensions which collapses Lagrangian three-spheres and replaces them by symplectic two-spheres. Under mirror symmetry it corresponds to an operation on complex 3-folds studied by Clemens, Friedman and Tian. We describe several examples which show that there are either many more Calabi-Yau manifolds (e.g. rigid ones) than previously thought or there exist ``symplectic Calabi-Yaus'' -- non-Kaehler symplectic 6-folds with c_1=0. The analogous surgery in four dimensions, with a generalisation to ADE-trees of Lagrangians, implies that the canonical class of a minimal complex surface contains symplectic forms if and only if it has positive square.
dc.descriptionCorrections for publication in J. Diff. Geom. and additions to examples. In particular, to date there are no examples proven to be non-Kaehler
dc.identifierhttps://arxiv.org/abs/math/0209319
dc.identifierhttp://arxiv.org/abs/math/0209319
dc.identifierJ.Diff.Geom. 62 (2002) 209-242
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/99228
dc.subjectSymplectic Geometry
dc.subject53D35; 14J32
dc.titleSymplectic conifold transitions
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