Extension of 2-forms and symplectic varieties
نویسنده
چکیده
In this paper we shall prove two theorems (Stability Theorem, Local Torelli Theorem) for symplectic varieties. Let us recall the notion of a symplectic singularity. Let X be a good representative of a normal singularity. Then the singularity is symplectic if the regular locus U of X admits an everywhere non-degenerate holomorphic closed 2-form ω where ω extends to a regular form on Y for a resolution of singularities Y → X . Similarly we say that a normal compact Kaehler space Z is a symplectic variety if the regular locus V of Z admits a non-degenerate holomorphic closed 2-form ω where ω extends to a regular form on Z̃, where Z̃ → Z is a resolution of singularities of Z. When Z has a resolution π : Z̃ → Z such that (Z̃, π∗ω) is a symplectic manifold, we call Z has a symplectic resolution.
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