Canonical surfaces of higher degree
  We consider a family of surfaces of general type $S$ with $K_S$ ample, having $K^2_S = 24, p_g (S) = 6, q(S)=0$. We prove that for these surfaces the canonical system is base point free and yields an embedding $\Phi_1 : S \rightarrow \mathbb{P}^5$.   This result answers a question posed by G. and M. Kapustka.   We discuss some related open problems, concerning also the case $p_g(S) = 5$, where one requires the canonical map to be birational onto its image. 
Fabrizio Catanese (Universitaet Bayreuth)
math.AG math.CV