Algebraic Curves: an Introduction to Algebraic Geometry
by William Fulton
Publisher: Benjamin 1969
Number of pages: 129
The aim of these notes is to develop the theory of algebraic curves from the viewpoint of modern algebraic geometry, but without excessive prerequisites. We have assumed that the reader is familiar with some basic properties of rings, ideals, and polynomials, such as is often covered in a one-semester course in modern algebra; additional commutative algebra is developed in later sections.
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by Caucher Birkar - arXiv
Topics covered: introduction into the subject, contractions and extremal rays, pairs and singularities, Kodaira dimension, minimal model program, cone and contraction, vanishing, base point freeness, flips and local finite generation, etc.
by Enrique Arrondo - Universidad Complutense de Madrid
The scope of these notes is to present a soft and practical introduction to algebraic geometry, i.e. with very few algebraic requirements but arriving soon to deep results and concrete examples that can be obtained 'by hand'.
by S. Basu, R. Pollack, M. Roy - Springer
The monograph gives a detailed exposition of the algorithmic real algebraic geometry. It is well written and will be useful both for beginners and for advanced readers, who work in real algebraic geometry or apply its methods in other fields.
by Michel Coste - Universite de Rennes
Semialgebraic geometry is the study of sets of real solutions of systems of polynomial equations and inequalities. These notes present the first results of semialgebraic geometry and related algorithmic issues. Their content is by no means original.