On the extendability of quadratic polynomial mappings of the plane
Volume 96 / 2009
Annales Polonici Mathematici 96 (2009), 283-294
MSC: Primary 30C99, 30D50, 30C10, 32H02; Secondary 32H50, 32D15, 30C62.
DOI: 10.4064/ap96-3-6
Abstract
We shall prove, using the result from our previous paper [Ann. Polon. Math. 88 (2006)], that for a quadratic polynomial mapping $Q$ of $\mathbb R^2$ only the geometric shape of the critical set of $Q$ determines whether the complexification of $Q$ can be extended to an endomorphism of $\mathbb C{\mathbb P}^2$. At the end of the paper we describe some interesting classes of quadratic polynomial mappings of $\mathbb R^2$ and give some examples.
