Roberto Pignatelli

Surfaces of general type with geometric genus zero: a survey

In the last years there have been several new constructions of surfaces of general type with pg = 0, and important progress on their classification. The present paper presents the status of the art on surfaces of general type with pg = 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.

QUOTIENTS OF PRODUCTS OF CURVES, NEW SURFACES WITH pg = 0 AND THEIR FUNDAMENTAL GROUPS

We construct many new surfaces of general type with

Complex Surfaces of General Type: Some Recent Progress

q=p_g = 0

The classification of minimal product-quotient surfaces with _{}=0.

whose canonical model is the quotient of the product of two curves by the action of a finite group

Canonical Rings of Surfaces Whose Canonical System has Base Points

G

New examples of Calabi-Yau threefolds and genus zero surfaces

, constructing in this way many new interesting fundamental groups which distinguish connected components of the moduli space of surfaces of general type. We indeed classify all such surfaces whose canonical model is singular (the smooth case was classified in an earlier work). As an important tool we prove a structure theorem giving a precise description of the fundamental group of quotients of products of curves by the action of a finite group

Product-quotient surfaces: new invariants and algorithms

G

The moduli space of even surfaces of general type with K2 = 8, pg = 4 , and q=0

.

Surfaces with

Chapters : Old and new inequalities; Surfaces with

K^{2}=8

\chi=1