The projective-space exceptional-locus conjecture for symplectic contractions

Let XX be a smooth projective symplectic variety of dimension 2n2n, and let

XZX\longrightarrow Z

be a birational contraction whose degenerate locus BB is contracted to isolated points. Projective-space exceptional-locus conjecture. The locus BB is a disjoint union of smooth subvarieties, each isomorphic to Pn{\Bbb P}^n. The result is known when a smooth subvariety is contracted to a point, but the stated assertion for an entire degenerate locus is presented as an expectation and remains open.

Sources & referencesView supporting material

Primary source

Yi Hu and S. -T. Yau, “HyperKähler Manifolds and Birational Transformations”, arXiv:math/0111089 (2003).

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