Abstract:

The study of the canonical map of surfaces of general type is a classical subject in the theory of algebraic surfaces. The canonical map was first studied by A. Beauville in 1979. He proved that if the image of the canonical map of a minimal surface of general type is a surface, this surface either has geometric genus zero (I) or is canonically embedded (II). Furthermore, he showed that the degree of the canonical map is less than or equal to 36. In the last decade, the problem of constructing examples of surfaces of general type with canonical map of high degree has been studied by many authors. Nonetheless, there still remain many questions left open. In this talk, we present some new examples of surfaces with non-birational canonical map in two classes (I), (II).