Algebraic Geometry, Abstract, Specialty Boutique 

This introduction to algebraic geometry assumes only the standard background of undergraduate algebra and is particularly suitable for those with no previous contact with the subject.The book focusses on projective algebraic geometry over an algebraically closed base field. It starts with easily-formulated problems with non-trivial solutions – for example, Bézout’s theorem and the problem of rational curves – and uses these problems to introduce the fundamental tools of modern algebraic geometry: dimension; singularities; sheaves; varieties; and cohomology. The treatment uses as little commutative algebra as possible by quoting without proof (or proving only in special cases) theorems whose proof is not necessary in practice, the priority being to develop an understanding of the phenomena rather than a mastery of the technique. A range of exercises is provided for each topic discussed, and a selection of problems and exam papers are collected in an appendix to provide material for further study. - from Amzon