| 概要 | Algebraic surfaces with vanishing geometric genus are interesting in
view of Castelnuovo's rationality criterion. This class of surfaces
has been studied extensively
by algebraic geometers and topologists for a long time. Although a
large number of non-simply connected complex surfaces of general
type with vanishing have
been known, the only previously known simply connected, minimal,
algebraic surface of general type with vanishing geometric genus was
Barlow surface.
In 2006, Jongil Park and I gave a new method to construct simply
connected algebraic surfaces of general type with vanishing
geometric genus via Q-Gorenstein
smoothing of a singular rational surface. Q-Gorenstein smoothing is
the rational blow-down surgery in the complex category. This
singular surface is obtained
by contraction of the chains of rational curves in the blowup of a
special rational elliptic surface. In this talk, I will present some
historical background of algebraic
surfaces with vanishing geometric genus, and explain ideas of
construction of surfaces of general type via Q-Gorenstein smoothing
and elliptic surfaces. |