Canonical surfaces in ${\mathbb{P}}^4$ with $p_g=p_a=5$ and $K^2=11$

Abstract

In [Böh] a structure theorem for Gorenstein algebras in codimension 2 was obtained. In the first part of this article we give a geometric application and prove a structure theorem for good birational canonical projections of regular surfaces of general type with $p_g=5$ to ${\mathbb{P}}^4$ (Theorem 1.6). In the second part we show how this can be used to analyze the moduli space of canonical surfaces with $q=0$, $p_g=5$ and $K^2=11$ (Theorem 2.4).