Computational Algebraic Geometry

Hal Schenck

194 pages, parution le 09/12/2003

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Résumé

The interplay between algebra and geometry is a beautiful (and fun!) area of mathematical investigation. Recent advances in computing and algorithms make it possible to tackle many classical problems in a down-to-earth and concrete fashion. This opens wonderful new vistas and allows us to pose, study and solve problems that were previously out of reach.

Suitable for graduate students, the objective of this book is to bring advanced algebra to life with lots of examples. The first chapters provide an introduction to commutative algebra and connections to geometry. The rest of the book focuses on three active areas of contemporary algebra:

Homological Algebra (the snake lemma, long exact sequence inhomology, functors and derived functors (Tor and Ext), and double complexes);
Algebraic Combinatorics and Algebraic Topology (simplicial complexes and simplicial homology, Stanley-Reisner rings, upper bound theorem and polytopes);
and Algebraic Geometry (points and curves in projective space, Riemann-Roch, Cech cohomology, regularity).

Preface
1. Basics of commutative algebra
2. Projective space and graded objects
3. Free resolutions and regular sequences
4. Gröbner bases
5. Combinatorics and topology
6. Functors: localization, hom, and tensor
7. Geometry of points
8. Homological algebra, derived functors
9. Curves, sheaves and cohomology
10. Projective dimension

A. Abstract algebra primer
B. Complex analysis primer
Bibliography

L'auteur - Hal Schenck

Texas A& M University

Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Hal Schenck
Parution	09/12/2003
Nb. de pages	194
Format	15,5 x 23
Couverture	Broché
Poids	280g
Intérieur	Noir et Blanc
EAN13	9780521536509
ISBN13	978-0-521-53650-9