Actions of \(SL_2(k)\) on affine \(k\)-domains and fundamental pairs

Vector bundles on surfaces and higher-dimensional varieties, and their moduli (14J60) Derivations and commutative rings (13N15) Group actions on affine varieties (14R20)

Cites Work

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Singular points of affine ML-surfaces
On the hypersurface \(x+x^2y+z^2+t^3=0\) in \(\mathbb{C}^4\) or a \(\mathbb{C}^3\)-like threefold which is not \(\mathbb{C}^3\)
Polynomials with general \(\mathbb{C}^ 2\)-fibers are variables.
The cylinder over the Koras-Russell cubic threefold has a trivial Makar-Limanov invariant
On free holomorphic \({\mathbb{C}}\)-actions on \({\mathbb{C}}^ n\) and homogeneous Stein manifolds
The classification of homogeneous surfaces
Semisimple group actions on the three dimensional affine space are linear
On Zariski problem
Affine surfaces containing cylinderlike open sets
On the absence of nontrivial separable forms of the affine plane
Propriétés topologiques des polynômes de deux variables complexes et automorphismes algébriques de l'espace \(C^2\)
Invariant rings and quasiaffine quotients
Locally nilpotent derivations and Danielewski surfaces
Real and rational forms of certain \({\text O}_2(\mathbb{C})\)-actions, and a solution to the weak complexification problem
Polyhedral divisors and \(SL_{2}\)-actions on affine \(T\)-varieties
A counterexample to Hilbert's fourteenth problem in dimension 5
Cable algebras and rings of \(\mathbb{G}_a\)-invariants
Foundations of invariant theory for the down operator
On the uniqueness of the coefficient ring in a polynomial ring
On the family of affine threefolds \(x^my = F(x,z,t)\)
Automorphism Groups of Certain Rational Hypersurfaces in Complex Four-Space
Ideals defined by matrices and a certain complex associated with them
A Note on Locally Nilpotent Derivations and Variables of k[X, Y, Z]
SEMISIMPLE AUTOMORPHISM GROUPS OF FOUR-DIMENSIONAL AFFINE SPACE
CLASSIFICATION OF AFFINE ALGEBRAIC SURFACES THAT ARE QUASIHOMOGENEOUS WITH RESPECT TO AN ALGEBRAIC GROUP
On actions of reductive groups with one-parameter family
On SL ₂ -actions of complexity one
Locally trivial 𝔾_a−actions on ℂ⁵ with singular algebraic quotients
The Geometry of Syzygies
QUASIHOMOGENEOUS AFFINE ALGEBRAIC VARIETIES OF THE GROUPSL(2)
On the classification of 3-dimensionalSL₂(ℂ)-varieties
AFFINE SURFACES WHICH ARE QUASIHOMOGENEOUS WITH RESPECT TO AN ALGEBRAIC GROUP
Algebraic theory of locally nilpotent derivations

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