A connection between birational automorphisms of the plane and linear systems of curves

作者：Perez Diaz Sonia^*; Blasco Angel

来源：Journal of Computational and Applied Mathematics, 2015, 283: 91-105.

DOI：10.1016/j.cam.2015.01.026

• Birationality
• Automorphism
• Linear systems of curves

In this paper, we prove that there exists a one-to-one correspondence between birational automorphisms of the plane and pairs of pencils of curves intersecting in a unique point. As a consequence, we show how to construct birational automorphisms of the plane of a certain degree d (fixed in advance) from some curves generating two linear systems of curves of degrees d and (d) over tilde, where (d) over tilde = d - 2 for d > 2, and (d) over tilde = 1 otherwise. In addition, we also get the inverse of the birational automorphism constructed, and we show that its degree is obtained from the degree of the linear system of curves. As a special case, we show how these results can be stated to polynomial birational automorphisms of the plane.

• 出版日期2015-8-1