Mariusz Koras


Singularities of homology planes of log general type


A surface $X$ is called a homology plane if the homology groups $H_i(X,\mathbb{Z})$ vanish for $i>0$. We prove that a normal homology plane of logarithmic Kodaira dimension equal $2$ has at most one singular point and that it is a cyclic quotient singularity. As a corollary we prove that the authomorphism group of a smooth homology plane of general type is cyclic. This is a joint work with R.V.Gurjar, M.Miyanishi and P.Russell.