Principles of algebraic geometry

a Comprehensive, Self-contained Treatment Presenting General Results Of The Theory. Establishes A Geometric Intuition And A Working Facility With Specific Geometric Practices. Emphasizes Applications Through The Study Of Interesting Examples And The Development Of Computational Tools. Coverage Ranges From Analytic To Geometric. Treats Basic Techniques And Results Of Complex Manifold Theory, Focusing On Results Applicable To Projective Varieties, And Includes Discussion Of The Theory Of Riemann Surfaces And Algebraic Curves, Algebraic Surfaces And The Quadric Line Complex As Well As Special Topics In Complex Manifolds. In this chapter we sketch the foundational material from several complex variables, complex manifold theory, topology, and differential geometry that will be used in our study of algebraic geometry.