Symplectic conifold transitions

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

We 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.
Corrections for publication in J. Diff. Geom. and additions to examples. In particular, to date there are no examples proven to be non-Kaehler

Keywords

Symplectic Geometry, 53D35; 14J32

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/99228

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0209319
 http://arxiv.org/abs/math/0209319
 J.Diff.Geom. 62 (2002) 209-242

Collections

arXiv