Introduction to Algebraic Geometry
Cambridge University Press, 5/3/2007
EAN 9780521691413, ISBN10: 0521691419
Paperback, 264 pages, 24.7 x 17.4 x 1.4 cm
Language: English
Algebraic geometry, central to pure mathematics, has important applications in such fields as engineering, computer science, statistics and computational biology, which exploit the computational algorithms that the theory provides. Users get the full benefit, however, when they know something of the underlying theory, as well as basic procedures and facts. This book is a systematic introduction to the central concepts of algebraic geometry most useful for computation. Written for advanced undergraduate and graduate students in mathematics and researchers in application areas, it focuses on specific examples and restricts development of formalism to what is needed to address these examples. In particular, it introduces the notion of Gröbner bases early on and develops algorithms for almost everything covered. It is based on courses given over the past five years in a large interdisciplinary programme in computational algebraic geometry at Rice University, spanning mathematics, computer science, biomathematics and bioinformatics.
Introduction
1. Guiding problems
2. Division algorithm and Gröbner bases
3. Affine varieties
4. Elimination
5. Resultants
6. Irreducible varieties
7. Nullstellensatz
8. Primary decomposition
9. Projective geometry
10. Projective elimination theory
11. Parametrizing linear subspaces
12. Hilbert polynomials and Bezout
Appendix. Notions from abstract algebra
References
Index.
'Yet another introduction to algebraic geometry? No! This is a book that has been missing from our textbook arsenal and that belongs on the bookshelf of anyone who plans to either teach or study algebraic geometry.' Sándor Kovács, University of Washington