# Canonical surfaces in <em><strong>P</strong><sup>4</sup></em> with <em>p<sub>g</sub>=p<sub>a</sub>=5</em> and <em>K<sup>2</sup>=11</em>

### Christian Böhning

Universität Hamburg, Germany

## Abstract

In \cite{Boh} 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).

## Cite this article

Christian Böhning, Canonical surfaces in <em><strong>P</strong><sup>4</sup></em> with <em>p<sub>g</sub>=p<sub>a</sub>=5</em> and <em>K<sup>2</sup>=11</em>. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 18 (2007), no. 1, pp. 39–57

DOI 10.4171/RLM/480