On Generalised Danielewski and Asanuma varieties

2022/08/30 by Parnashree Ghosh, Ghosh, Parnashree, Neena Gupta +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Advanced Topics in Algebra

paper · pdf · doi:10.48550/arxiv.2208.14238

Abstract

In this paper we extend a result of Dubouloz on the Cancellation Problem in higher dimensions (\geqslant 2) over the field of complex numbers to fields of arbitrary characteristic. We then apply the generalised result to describe the Makar-Limanov and Derksen invariant of generalised Asanuma varieties under certain hypotheses. We also establish a necessary and sufficient condition for certain generalised Asanuma varieties to be isomorphic to polynomial rings.

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