Around the Abhyankar--Sathaye conjecture
Vladimir L. Popov
TL;DR
This paper proves a rational version of a strengthened conjecture related to commuting derivations and develops a systematic method to construct counterexamples in higher dimensions, addressing a question by M. El Kahoui.
Contribution
It introduces a rational form of the conjecture, removes the commutativity assumption, and provides a systematic construction method for counterexamples in dimensions greater than three.
Findings
Proved a rational version of the strengthened Commuting Derivation Conjecture.
Developed a systematic method for constructing counterexamples in higher dimensions.
Addressed and answered a question posed by M. El Kahoui.
Abstract
A "rational" version of the strengthened form of the Commuting Derivation Conjecture, in which the assumption of commutativity is dropped, is proved. A systematic method of constructing in any dimension greater than 3 the examples answering in the negative a question by M. El Kahoui is developed.
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