8 citations · 21 across the 14 of their papers we have counts for
14 papers
Automorphisms of the ring of invariants of the binary quintic representation of SL2
Daniel Daigle, Gene Freudenburg
Let k^[6] denote a polynomial ring in 6 variables over an algebraically closed field k of characteristic zero and consider the action of SL2(k) on k^[6] induced by the irreducible…
A Criterion for the Density Property of Stein Manifolds
Rafael B. Andrist, Gene Freudenburg, Gaofeng Huang +2
We generalize a criterion for the density property of Stein manifolds. As an application, we give a new, simple proof of the fact that the Danielewski surfaces have the algebraic d…
Affine and Unirational unique factorial domains with unmixed gradings
Gene Freudenburg, Takanori Nagamine
This paper studies the class of unique factorial domains over an algebraically closed field which are affine or unirational over and which admit an effective unmixed $\…
Generalizations of Samuel's criteria for a ring to be a unique factorization domain
Daniel Daigle, Gene Freudenburg, Takanori Nagamine
We give several criteria for a ring to be a UFD including generalizations of some criteria due to P. Samuel. These criteria are applied to construct, for any field k, (1) a Z-grade…
Smooth factorial affine surfaces of logarithmic Kodaira dimension zero with trivial units
Gene Freudenburg, Hideo Kojima, Takanori Nagamine
This paper considers the family of smooth affine factorial surfaces of logarithmic Kodaira dimension 0 with trivial units over an algebraically closed field . Ou…
Factorial rational varieties which admit or fail to admit an elliptic -action
Gene Freudenburg, Takanori Nagamine
Over a field , we study rational UFDs of finite transcendence degree over . We classify such UFDs when , is algebraically closed, and admits a positive $…
Algebraic vector bundles on the 2-sphere and smooth rational varieties with infinitely many real forms
Adrien Dubouloz, Gene Freudenburg, Lucy Moser-Jauslin
We construct smooth rational real algebraic varieties of every dimension 4 which admit infinitely many pairwise non-isomorphic real forms.
The polar group of a real form of an affine or projective -variety
Gene Freudenburg
A general problem is to classify the real forms of a complex variety up to isomorphism. This paper introduces the polar group of a real form of a complex variety as a tool…
On the uniqueness of polynomial embeddings of the real 1-sphere in the plane
Gene Freudenburg
This paper considers real forms of closed algebraic -embeddings in . The classification of such embeddings was recently completed by Cassou-Nogues, Kora…
Canonical factorization of the quotient morphism for an affine -variety
Gene Freudenburg
Working over a ground field of characteristic zero, this paper studies the quotient morphism for an affine -variety with affine quotient . It is sho…
Cable algebras and rings of -invariants
Gene Freudenburg, Shigeru Kuroda
For a field , the ring of invariants of an action of the unipotent -group on an affine -variety is quasi-affine, but not generally affine. Cable algebras are introdu…
An affine version of a theorem of Nagata
Gene Freudenburg
Let R be an affine k-domain over the field k. The paper's main result is that, if R admits a non-trivial embedding in a polynomial ring K[s] for some field K containing k, then R c…
Laurent cancellation for rings of transcendence degree one
Gene Freudenburg
If is an integral domain and is an -algebra, then has the {\it Laurent cancellation property over } if implies ($n\ge…
Curves defined by Chebyshev polynomials
Gene Freudenburg, Jenna Freudenburg
Working over a field $\kk$ of characteristic zero, this paper studies line embeddings of the form $ϕ= (T_i,T_j,T_k):\A^1\to\A^3$, where denotes the degree Chebyshev polyn…