Polynomial Models of Degree 5 and Algebras of Their Automorphisms

In classifying and studying holomorphic automorphisms of surfaces, it is often convenient to pass to tangent model surfaces. This method is well developed for surfaces of type $(n,K)$, where $K\le n^2$; for such surfaces, tangent quadrics (i.e., surfaces determined by equations of degree 2) with a number of useful properties have been constructed. In recent years, for surfaces of higher codimensions, tangent model surfaces of degrees 3 and 4 with similar properties were constructed. However, this construction imposes new constraints on the codimension. In this paper, the same method is applied to surfaces of even higher codimension. Model surfaces of the fifth degree are constructed. It is shown that all the basic useful properties of model surfaces are preserved, in spite of a number of technical difficulties.