We consider minimal surfaces of general type whose canonical map is "special" meaning that it is composed of a pencil or its degree is high. We characterize, to some extent, Beauville's examples of irregularity 2 in the pencil case, and show that the irregularity is at most 12 when the canonical degree is 5.
Cite this article
Kazuhiro Konno, On the Irregularity of Special Non-Canonical Surfaces. Publ. Res. Inst. Math. Sci. 30 (1994), no. 4, pp. 671–688DOI 10.2977/PRIMS/1195165794