# Surface links

### Chapters on algebraic surfaces, Park City 1993
index

### 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

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.

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