Algebraic Geometry

Algebraic Curves
An overview.
http://www.geom.uiuc.edu/docs/reference/CRC-formulas/node33.html

Algebraic Geometry Notebooks for Non-Experts
By Aksel Sogstad. Short introductory sketch of some topics in the algebraic geometry of curves.
http://www.sogstad.net/algnotes/

The Brill-Noether Project
Aims to answer the basic questions this theory B(n,d,k) for vector bundles on algebraic curves. Welcomes contributions.
http://www.liv.ac.uk/~newstead/bnt.html

The Cubic Surface Homepage
Images, software, links. At the University of Mainz, Germany.
http://enriques.mathematik.uni-mainz.de/csh/

Differential Algebraic Geometry - A Scheme-theoretic Approach
Slides in multimedia format from a lecture by Henri Gillet at MSRI.
http://www.msri.org/publications/ln/msri/1998/mtf/gillet/1/

The Hodge Conjecture
A description of the conjecture by Deligne (PDF) and details of the prize offered for its resolution.
http://www.claymath.org/prizeproblems/hodge.htm

Introduction to Algebraic Geometry
Illustrated webnotes by Donu Arapura.
http://www.math.purdue.edu/~dvb/algeom.html

Noncommutative Geometry and Algebra
People, groups and publications. Compiled by Paul Smith, University of Washington.
http://www.math.washington.edu/~smith/Research/research.html