Projective equivalence of homogeneous binary polynomials (Q1824665)

The aim is to define new sets of invariants for complex projective equivalence \({\mathcal E}_ p\) defined on the set \({\mathbb{C}}_ k\) of complex homogeneous binary polynomials of fixed degree k. It will be shown that the characterization of the class \({\mathcal E}_ p(f)\) by invariants is equivalent to a problem of algebraic projective geometry: find the necessary and sufficient conditions under which two sets of points of \({\mathbb{C}}\cup \{\infty \}\) may be mapped under a projective transformation \(\beta\in PGL(1,{\mathbb{C}})\).