By Daniel Perrin (auth.)
Aimed essentially at graduate scholars and starting researchers, this booklet presents an creation to algebraic geometry that's really compatible for people with no past touch with the topic and assumes simply the normal history of undergraduate algebra. it truly is constructed from a masters direction given on the Université Paris-Sud, Orsay, and focusses on projective algebraic geometry over an algebraically closed base field.
The booklet starts off with easily-formulated issues of non-trivial suggestions – for instance, Bézout’s theorem and the matter of rational curves – and makes use of those difficulties to introduce the elemental instruments of contemporary algebraic geometry: measurement; singularities; sheaves; forms; and cohomology. The remedy makes use of as little commutative algebra as attainable through quoting with out evidence (or proving simply in detailed situations) theorems whose facts isn't beneficial in perform, the concern being to improve an realizing of the phenomena instead of a mastery of the procedure. various workouts is supplied for every subject mentioned, and a variety of difficulties and examination papers are amassed in an appendix to supply fabric for additional study.