Mathematical Research Letters
Volume 12, Issue 5, September 2005 pp. 767-778.
Conifold transitions and Mori theoryAuthors: Alessio Corti (1) and Ivan Smith (2)
Author institution: Imperial College London (1) and Cambridge (2)
Summary: 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.
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