David R. Finston

Ga actions on Cn

Rational actions of the additive group of complex numbers on complex n space are considered. A ring theoretic criterion for properness is given, along with ideal theoretic criteria for local triviality of such actions. The relationship between local triviality and flatness of the polynomial ring over its subring of Ga invariants is investigated.

On exotic affine 3-spheres

Every

Constructing (Almost) Rigid Rings and a UFD Having Infinitely Generated Derksen and Makar-Limanov Invariants

\mathbb{A}^{1}-

Centralizers of locally nilpotent derivations

bundle over the complex affine plane punctured at the origin, is trivial in the differentiable category but there are infinitely many distinct isomorphy classes of algebraic bundles. Isomorphy types of total spaces of such algebraic bundles are considered; in particular, the complex affine 3-sphere admitts such a structure with an additional homogeneity property. Total spaces of nontrivial homogeneous

Proper triangular a-actions on 4 are translations

\mathbb{A}^{1}

G a Invariants and Slices

-bundles over the punctured plane are classified up to

Additive group actions with finitely generated invariants

\mathbb{G}_{m}

Determining local triviality of G a actions

-equivariant algebraic isomorphism and a criterion for nonisomorphy is given. In fact the affine 3-sphere is not isomorphic as an abstract variety to the total space of any

Calculus Instruction at New Mexico State University through Weekly Themes and Cooperative Learning.

\mathbb{A}^{1}

Algebras and differential equations with additive symmetry

-bundle over the punctured plane of different homogeneous degree, which gives rise to the existence of exotic spheres, a phenomenon that first arises in dimension three. As a by product, an example is given of two biholomorphic but not algebraically isomorphic threefolds, both with a trivial Makar-Limanov invariant, and with isomorphic cylinders.