Conifold transitions and Mori theory

Details Conifold transitions and Mori theory Conifold transitions and Mori theory

2005-01-04

arxiv.org/abs/math/0501043v2

Mathematics

Symplectic Geometry

16 pages, no figures. Version 2 has minor referee's corrections; this version to appear in Mathematical Research Letters

Scientific paper

We show there is a symplectic conifold transition of a projective 3-fold which is not deformation equivalent to any Kaehler manifold. The key ingredient is Mori's classification of extremal rays on smooth projective 3-folds. It follows that there is a Lagrangian sphere in a projective variety which is not the vanishing cycle of any Kaehler degeneration, answering a question of Donaldson.

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