### ECM4 Stockholm, Jul 2004 lecture

Constructing algebraic varieties via commutative algebra, in Proc. of 4th
European Congress of Math (Stockholm 2004), European Math Soc. 2005,
pp. 655--667. The lecture, on behalf of the EAGER network, was an
introduction to graded ring methods and its application to algebraic
surfaces, esp. in the works of European geometers since Fano and Enriques.
The preprint is 22 pages of OHP slides available as pdf or ps files.

### More chapters (in preparation)

The book will be in the same style as the 1993 Park City [Chapters], with
beginning graduate students, followed by an unsystematic run through some
technical prerequisites, intended to help those suffering more systematic
texts, plus more substantial chapters based on research in algebraic
surfaces, together with exercises and open problems.

Some of these chapters remain incomplete -- the gaps providing potential
research projects. I have several other half-written chapters for anyone who
wants to join me as co-author.

Cyclic surface quotient singularities
Du Val surface singularities
See the Homework for the first and third of these chapters.

Surfaces with p_g=3, K^2=4 according to Horikawa and Dicks
Compare also Ingrid Bauer, Fabrizio Catanese and Roberto Pignatelli, Canonical
rings of surfaces whose canonical system has base points,  abstractpdf file (45 pp.)
and Ingrid Bauer, Surfaces with K^2 = 7 and p_g = 4, Mem. Amer. Math. Soc.,
vol. 152, no. 721, 2001

Surfaces with p_g = 0, K^2 = 1, J. Fac. Sci. Tokyo Univ. 25 (1978), 75--92
Godeaux and Campedelli surfaces
A simply connected surface of general type with p_g=0, K^2=1 due to Rebecca Barlow
Surfaces with p_g=0, K^2=2
Infinitesimal view of extending a hyperplane section, in: Algebraic Geometry
-- Hyperplane sections and related topics (L'Aquila 1988), Springer LNM 1417
(1990), 214--286
Problems in geography of surfaces
See also T. Ashikaga and K. Konno, Global and local properties of pencils of
algebraic curves, Adv. Stud. in Pure Math. 2 (2000), 1-49. pdf file.
See also Elisa Tenni, Fibred surfaces with general pencils of genus 5,
preprint arXiv:0804.0388.