An algorithmic approach to the Polydegree Conjecture for plane polynomial automorphisms |
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Affiliation: | 1. Department of Mathematics and Statistics, University of South Alabama, United States of America;2. Department of Mathematics, Wingate University, United States of America;1. University of Science – Ho Chi Minh City, Faculty of Math & Computer Science, 227 Nguyen Van Cu St., District 5, Ho Chi Minh City, Viet Nam;2. Mathematics Research Unit of Université du Luxembourg, Maison du Nombre, 6, Avenue de la Fonte, L-4364 Esch-sur-Alzette, Luxembourg;3. Institut für Mathematik, Universität Osnabrück, Albrechtstraße 28a, 49076 Osnabrück, Germany |
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Abstract: | We study the interaction between two structures on the group of polynomial automorphisms of the affine plane: its structure as an amalgamated free product and as an infinite-dimensional algebraic variety. We introduce a new conjecture, and show how it implies the Polydegree Conjecture. As the new conjecture is an ideal membership question, this shows that the Polydegree Conjecture is algorithmically decidable. We further describe how this approach provides a unified and shorter method of recovering existing results of Edo and Furter. |
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Keywords: | 14R10 |
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