Introduces the relative Rees algebra of Ga,S-actions on relative affine schemes, establishes its basic properties, and applies it to examples from locally nilpotent derivations and families of affine threefolds.
Exotic Ga-quotients of SL$_2 \times \mathbb{A}^1$
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abstract
Every deformed Koras-Russell threefold of the first kind $Y = \left\{ x^{n}z=y^{m}-t^{r} + xh(x,y,t)\right\}$ in $\mathbb{A}^{4}$ is the algebraic quotient of proper Zariski locally trivial $\mathbb{G}_a$-action on $\mathrm{SL}_2 \times \mathbb{A}^1$.
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2019 1verdicts
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Rees algebras of additive group actions
Introduces the relative Rees algebra of Ga,S-actions on relative affine schemes, establishes its basic properties, and applies it to examples from locally nilpotent derivations and families of affine threefolds.