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1 vote
2 answers
341 views

Small contraction for Hyperkähler Varieties

I have the following basic question. Everything is over $\mathbb{C}$. Let $X$ be a hyperkähler (irreducible holomorphic symplectic) variety and we consider a small contraction $f\colon X \rightarrow ...
4 votes
0 answers
102 views

Existence of a rational curve in the center of a birational contraction for symplectic singularities

Let $M$ be a holomorphically symplectic complex manifold, and $f: M \to X$ a holomorphic, birational contraction to a Stein variety $X$, contracting a subvariety $E$ to a point, and bijective outside ...