Non-smoothable varieties.
We show that a complex normal surface singularity admitting a contracting automorphism is necessarily quasihomogeneous. We also describe the geometry of a compact complex surface arising as the orbit space of such a contracting automorphism.
We give explicit constructions of all the numerical Campedelli surfaces, i.e. the minimal surfaces of general type with and , whose fundamental group has order 9. There are three families, one with and two with . We also determine the base locus of the bicanonical system of these surfaces. It turns out that for the surfaces with and for one of the families of surfaces with the base locus consists of two points. To our knowlegde, these are the only known examples of surfaces of general...
In this paper, we give a numerical characterization of nef arithmetic -Cartier divisors of -type on an arithmetic surface. Namely an arithmetic -Cartier divisor of -type is nef if and only if is pseudo-effective and .