Extends the LLV algebra to primitive symplectic varieties with isolated singularities via an isomorphism g ≅ so((IH²(X,Q), Q_X) ⊕ h) and studies the resulting representation theory with applications to the P=W conjecture.
Infinitesimal Variation of Harmonic Forms and Lefschetz Decomposition
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abstract
This paper studies the infinitesimal variation of the Lefschetz decomposition associated with a compatible sl_2-representation on a graded algebra. This allows to prove that the Jordan-Lefschetz property holds infinitesimally for the Kaehler Lie algebra (introduced by Looijenga and Lunts) of any compact Kaehler manifold. As a second application we describe how the space of harmonic forms changes when a Ricci-flat Kaehler form is deformed infinitesimally.
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The LLV Algebra for Primitive Symplectic Varieties with Isolated Singularities
Extends the LLV algebra to primitive symplectic varieties with isolated singularities via an isomorphism g ≅ so((IH²(X,Q), Q_X) ⊕ h) and studies the resulting representation theory with applications to the P=W conjecture.