161 research outputs found
Inductive characterizations of hyperquadrics
We give two characterizations of hyperquadrics: one as non-degenerate smooth
projective varieties swept out by large dimensional quadric subvarieties
passing through a point; the other as -manifolds with large secant
defects
Symplectic Resolutions for Coverings of Nilpotent Orbits
Let \0 be a nilpotent orbit in a semisimple complex Lie algebra \g.
Denote by the simply connected Lie group with Lie algebra \g. For a
-homogeneous covering M \to \0, let be the normalization of \bar{\0}
in the function field of . In this note, we study the existence of
symplectic resolutions for such coverings
Symplectic resolutions for nilpotent orbits (II)
We prove that for any two projective symplectic resolutions and
for a nilpotent orbit closure in a complex simple Lie algebra of classical
type, then is deformation equivalen to .Comment: An error is corrected, and the affirmation is weakene
A survey on symplectic singularities and resolutions
This is a survey written in an expositional style on the topic of symplectic
singularities and symplectic resolutions, which could also serve as an
introduction to this subject
Mukai flops and deformations of symplectic resolutions
We prove that two projective symplectic resolutions of \cit^{2n}/G are
connected by Mukai flops in codimension 2 for a finite sub-group G < \Sp(2n).
It is also shown that two projective symplectic resolutions of \cit^4/G are
deformation equivalent
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