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Free C+ actions on affine threefolds
Get PDFWe study algebraic actions of the additive group C+ on an affine threefold X and prove a smoothness property for the quotient morphism X -< X//C+. Then, following Shulim Kaliman, we give a proof of the conjecture that every free C+ action on affine 3-space C^3 is a translation
LINES IN AFFINE TORIC VARIETIES
No full textWe prove that up to automorphisms of the target the affine line A(1) admits a unique embedding into the regular part of an affine simplicial toric variety of dimension at least 4 which is smooth in codimension 2. This is an analog of the well-known result on the existence of a linearization of any polynomial embedding A(1) hooked right arrow A(n) for n >= 4
On the Jacobian conjecture
No full textWe show that the Jacobian conjecture can be reduced to a weaker conjecture in which all fibers of coordinate functions are irreducible.</p
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