Contents Online
Mathematical Research Letters
Volume 12 (2005)
Number 5
Conifold transitions and Mori theory
Pages: 767 – 778
DOI: https://dx.doi.org/10.4310/MRL.2005.v12.n5.a13
Authors
Abstract
We show there is a symplectic conifold transition of a projective 3-fold which is not deformation equivalent to any Kähler manifold. The key ingredient is Mori’s classification of extremal rays on smooth projective 3-folds. It follows that there is a (nullhomologous) Lagrangian sphere in a projective variety which is not the vanishing cycle of any Kähler degeneration, answering a question of Donaldson.
Published 1 January 2005