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.
The book will be in the same style as the 1993 Park City [Chapters], with
elementary chapters early on, suitable for advanced undergraduates and
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
Graded
rings
See the
Homework
for the first and third of these chapters.
Graded rings over K3 surfaces (See also later paper
math.AG/0202092)
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,
abstract,
pdf 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.