On double Danielewski varieties

2023/12/28 by Sun, Xiaosong, Zeng, Shuai
#13N15 #14R10 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2312.16808

Abstract

In this paper, we study the double Danielewski varieties which arose from the research on the classical Cancellation Problem. We describe the Makar-Limanov invariant and locally nilpotent derivations of these varieties. And in a subsequent paper we will describe the automorphisms groups of the varieties and verify that the varieties are counterexamples to the Cancellation Problem.

Related

• Isomorphism classes and stably isomorphisms of double Danielewski varieties
• Automorphisms of Danielewski varieties
• On Generalised Danielewski and Asanuma varieties
• Cancellation problem via locally nilpotent derivations
• Additive group actions on Danielewski varieties and the Cancellation Problem