Coble surfaces: projective models and automorphisms, with related topics

We study some properties of Coble surfaces, first introduced in 1919 by A. Coble. By definition, a complex Coble surface is a smooth rational projective surface over the complex numbers, with no anti - canonical divisor, and exactly one anti - bicanonical curve C. After a brief summary on the general properties of Coble surfaces, we focus our attention on the family of unnodal Coble surfaces with irreducible Coble curve. Under this assumptions, our main results are the following: any isotropic sequence of length smaller or equal than 8 can be extended to a sequence of length 10. Morever, there are no involutions which point - wise fix the curve C, and any involution is a lift of a Bertini involution.