Symplectic conifold transitions
I. Smith, R. P. Thomas, S. -T. Yau
Abstract
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 c1=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.
Create a lesson
Related papers
On some rigidity results for high-dimensional confoliations
Fabio Gironella, Seungook Yu
Holomorphic approximation for Hamiltonian diffeomorphism groups via the Symplectic Density Property
Gaofeng Huang, Frank Kutzschebauch
Open WDVV equations for non-commutative families of bounding cochains
Elad Kosloff
Invariant sets and spectral rigidity of Hamiltonian diffeomorphisms
Habib Alizadeh, Egor Shelukhin
Kuranishi spaces in a category of fibrant objects and their homotopy fiber products
Taesu Kim
Bi-contact plugs and dynamical hyperbolicity
Surena Hozoori