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Conifold transitions and Mori theory

Alessio Corti·Ivan Smith
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Abstract

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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Alessio Corti, Ivan Smith. 2005-01-04. Conifold transitions and Mori theory. https://arxiv.org/abs/math/0501043

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