Surfaces of general type with geometric genus zero: a survey

Ingrid Bauer, Fabrizio Catanese, Roberto Pignatelli

Published 2010-04-15, updated 2010-10-18Version 3

In the last years there have been several new constructions of surfaces of general type with $p_g=0$, and important progress on their classification. The present paper presents the status of the art on surfaces of general type with $p_g=0$, and gives an updated list of the existing surfaces, in the case where $K^2= 1,...,7$. It also focuses on certain important aspects of this classification.