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On the Variety of Automorphisms of the Affine Plane

✍ Scribed by Jean-Philippe Furter

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 273 KB
Volume: 195
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1997.7054

No coin nor oath required. For personal study only.

✦ Synopsis

The main subject of our study is GA , the variety of automophisms of the 2, n affine plane of degree bounded by a positive integer n. After detailing some definitions and notations in Section 1, we give in Section 2 an algorithm to decide whether an endomorphism of the affine plane over an integral domain is a tame automorphism. Then, by applying this algorithm to the Nagata automorphism, we recover easily its known results. In Section 6, we compute the number of irreducible components of GA when n F 9 and we show that GA is reducible

when n G 4. Our proofs are based on a precise decomposition theorem for automorphisms given in Section 3 and a characterization of length one automorphisms given in Section 5. Finally, in Section 7, we give some details on the case n s 4.

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