ar X iv : m at h / 03 09 12 5 v 1 [ m at h . A G ] 7 S ep 2 00 3 Birational morphisms of the plane
نویسندگان
چکیده
Let A be the affine plane over a field K of characteristic 0. Birational morphisms of A are mappings A → A given by polynomial mappings φ of the polynomial algebra K[x, y] such that for the quotient fields, one has K(φ(x), φ(y)) = K(x, y). Polynomial automorphisms are obvious examples of such mappings. Another obvious example is the mapping τx given by x → x, y → xy. For a while, it was an open question whether every birational morphism is a product of polynomial automorphisms and copies of τx. This question was answered in the negative by P. Russell (in an informal communication). In this paper, we give a simple combinatorial solution of the same problem. More importantly, our method yields an algorithm for deciding whether a given birational morphism can be factored that way.
منابع مشابه
ar X iv : h ep - t h / 01 03 09 3 v 1 1 3 M ar 2 00 1 Physical Aspects of the Space - Time Torsion
متن کامل
ar X iv : m at h / 04 09 00 4 v 1 [ m at h . A G ] 1 S ep 2 00 4 CAYLEY GROUPS
The classical Cayley map, X → (In − X)(In + X) −1 , is a birational iso-morphism between the special orthogonal group SOn and its Lie algebra son, which is SOn-equivariant with respect to the conjugating and adjoint actions respectively. We ask whether or not maps with these properties can be constructed for other algebraic groups. We show that the answer is usually " no " , with a few exceptio...
متن کاملar X iv : h ep - t h / 01 03 09 5 v 1 1 3 M ar 2 00 1 Pre - big bang in M - theory ∗
We discuss a simple cosmological model derived from M-theory. Three assumptions lead naturally to a pre-big bang scenario: (a) 11-dimensional supergravity describes the low-energy world; (b) non-gravitational fields live on a three-dimensional brane; and (c) asymptotically past triviality. Pac(s) numbers: 98.80.Bp, 04.65.+e, 98.80.Hw, 04.50.+h
متن کاملar X iv : m at h / 04 09 02 9 v 1 [ m at h . A G ] 2 S ep 2 00 4 ACM BUNDLES ON GENERAL HYPERSURFACES IN P 5 OF LOW DEGREE
In this paper we show that on a general hypersurface of degree r = 3, 4, 5, 6 in P 5 a rank 2 vector bundle E splits if and only if h 1 E(n) = h 2 E(n) = 0 for all n ∈ Z. Similar results for r = 1, 2 were obtained in [15], [16] and [1].
متن کامل