Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

On automorphisms of Danielewski surfaces


Author: Anthony J. Crachiola
Journal: J. Algebraic Geom. 15 (2006), 111-132
DOI: https://doi.org/10.1090/S1056-3911-05-00414-5
Published electronically: May 12, 2005
MathSciNet review: 2177197
Full-text PDF

Abstract | References | Additional Information

Abstract: Let $\mathbf{k}$ be any field. Let $R = \mathbf{k}[X,Y,Z]/(X^n Y - Z^2 - h(X)Z)$, where $h(0) \ne 0$ and $n \geq 2$. We develop techniques for computing the AK invariant of a domain with arbitrary characteristic. We use these techniques to compute $\operatorname{AK}(R)$, describe the automorphism group of $R$, and describe the isomorphism classes of these algebras. We then show that these algebras provide counterexamples to the cancellation problem over any field, extending Danielewski's original counterexample.


References [Enhancements On Off] (What's this?)


Additional Information

Anthony J. Crachiola
Affiliation: Department of Mathematical Sciences, Saginaw Valley State University, 7400 Bay Road, University Center, Michigan 48710
Email: crachiola@member.ams.org

DOI: https://doi.org/10.1090/S1056-3911-05-00414-5
Received by editor(s): November 15, 2004
Published electronically: May 12, 2005

American Mathematical Society