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Symplectic singularities
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We discuss a particular class of rational Gorenstein singularities, which we call symplectic. A normal variety V has symplectic singularities if its smooth part carries a closed symplectic 2-form whose pull-back in any resolution X --> V extends to a holomorphic 2-form on X . Our main result is the classification of isolated symplectic singularities with smooth projective tangent cone. They are in one-to-one correspondence with simple complex Lie algebras: to a Lie algebra g corresponds the singularity at 0 of the closure of the minimal (nonzero) nilpotent adjoint orbit in g .
Forward citations
Cited by 3 Pith papers
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Vertex Superalgebras for Hypertoric Varieties and 3d Abelian Gauge Theories
Constructs ħ-adic sheaves of vertex superalgebras on hypertoric varieties, proves the associated affine variety recovers the singular hypertoric one, establishes the 3d Higgs branch conjecture for abelian cases, and s...
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Orthosymplectic Chern-Simons Matter Theories: Global Forms, Dualities, and Vacua
A magnetic quiver framework is introduced to extract maximal branches and global forms of 3d orthosymplectic Chern-Simons matter theories from brane configurations, with global data fixed via indices and Hilbert series.
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Central Charges and Vacuum Moduli of 2d $\mathcal{N}=(0,4)$ Theories from Class $\mathcal{S}$
Proposes conjectural central charge formulas for 2d N=(0,4) theories from class S reductions and verifies agreement via Hilbert series on special and twisted Higgs branches for SU(2) cases.
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