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Lie algebras of zero divergence vector fields on complex affine algebraic varieties
Fabrizio Donzelli
For a smooth manifold equipped with a volume form, let $\dL$ be the Lie algebra of volume preserving smooth vector fields on . A. Lichnerowicz proved that the abelianization…
Makar-Limanov invariant, Derksen invariant, flexible points
Fabrizio Donzelli
We estabilish some connections among the Makar-Limanov invariant, the Derksen invariant, and the existence of flexible points on an affine variety.
Algebraic density property of Danilov-Gizatullin surfaces
Fabrizio Donzelli
A Danilov-Gizatullin surface is an affine surface which is the complement of an ample section of a Hirzebruch surface. The remarkable theorem of Danilov and Gizatullin stat…
Algebraic density property of homogeneous spaces
Fabrizio Donzelli, Alexander Dvorsky, Shulim Kaliman
Let be an affine algebraic variety with a transitive action of the algebraic automorphism group. Suppose that is equipped with several non-degenerate fixed point free $SL_2…