Algebraic Geometry

Aimed primarily at graduate students and beginning researchers, this book provides an introduction to algebraic geometry that is particularly suitable for those with no previous contact with the subject; it assumes only the standard background of undergraduate algebra. The book starts with easily-formulated problems with non-trivial solutions and uses these problems to introduce the fundamental tools of modern algebraic geometry: dimension; singularities; sheaves; varieties; and cohomology. 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.

Affine algebraic sets Projective algebraic sets Sheaves and varieties Dimension Tangent spaces and singular points Bézout's theorem Sheaf cohomology Arithmetic genus of curves and the weak Riemann-Roch theorem Rational maps, geometric genus and rational curves Liaison of space curves

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