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Book Review
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Book Information
Author(s):
H. Schenck
Title:
Computational algebraic geometry
Additional book information:
London Mathematical Society Student Texts, vol. 58,
Cambridge University Press, Cambridge,
2003,
xiv+ 193 pp.,
(hardback)
$70.00,
ISBN 0-521-82964-X
;
(paperback)
$28.00,
ISBN 0-521-53650-2
References:
-
- 1.
- W. Adams and P. Loustaunau, An Introduction to Gröbner Bases, Graduate Studies in Math. 3, AMS, Providence, 1994. MR 1287608 (95g:13025)
- 2.
- T. Becker and V. Weispfenning, Gröbner Bases: A Computational Approach to Commutative Algebra, Graduate Texts in Math. 141, Springer-Verlag, New York, Heidelberg, Berlin, 1993. MR 1213453 (95e:13018)
- 3.
- CoCoA, available at http://cocoa.dima.unige.it/.
- 4.
- D. Cox, J. Little, and D. O'Shea, Ideals, Varieties and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, Second Edition, Undergraduate Texts in Math., Springer-Verlag, New York, Heidelberg, Berlin, 1997. MR 1417938 (97h:13024)
- 5.
- D. Eisenbud, Commutative Algebra with a View Toward Algebraic Geometry, Graduate Texts in Math. 150, Springer-Verlag, New York, Heidelberg, Berlin, 1995. MR 1322960 (97a:13001)
- 6.
- D. Eisenbud and J. Harris, The Geometry of Schemes, Graduate Texts in Math. 197, Springer-Verlag, New York, Heidelberg, Berlin, 2002. MR 1730819 (2001d:14002)
- 7.
- D. Eisenbud, D. Grayson, M. Stillman, and B. Sturmfels (editors), Computations in Algebraic Geometry with Macaulay 2, Algorithms and Computations in Math. 8, Springer-Verlag, New York, Heidelberg, Berlin, 2002. MR 1949544 (2004b:14002)
- 8.
- G.-M. Greuel and G. Pfister, A Singular Introduction to Commutative Algebra, Springer-Verlag, New York, Heidelberg, Berlin, 2002. MR 1930604 (2003k:13001)
- 9.
- P. Griffiths and J. Harris, Principles of Algebraic Geometry, Series in Pure & Applied Mathematics, Wiley, New York, 1978. MR 0507725 (80b:14001)
- 10.
- A. Grothendieck and J. Dieudonné, Éléments de Géométrie Algébrique, Publications mathématiques d'IHES 4, 8, 11, 17, 20, 24, 28, 32, Bures-sur-Yvette, 1960-1967. Scanned versions available at http://grothendieck-circle.org/. The first volume (in a second edition) published as Éléments de Géométrie Algébrique I, Grundlehren der mathematischen Wissenschaften 166, Springer-Verlag, New York, Heidelberg, Berlin, 1971. MR 0217083 (36:177a); MR 0163909 (29:1208); MR 0163910 (29:1209); MR 0163911 (29:1210); MR 0173675 (30:3885); MR 0199181 (33:7330); MR 0217086 (36:178); MR 0238860 (39:220)
- 11.
- J. Harris, Algebraic Geometry, Graduate Texts in Math. 133, Springer-Verlag, New York, Heidelberg, Berlin, 1992. MR 1182558 (93j:14001)
- 12.
- R. Hartshorne, Algebraic Geometry, Graduate Texts in Math. 52, Springer-Verlag, New York, Heidelberg, Berlin, 1977. MR 0463157 (57:3116)
- 13.
- K. Hulek, Elementary Algebraic Geometry, Student Mathematical Library 20, AMS, Providence, 2003. Translation of Elementare Algebraische Geometrie, Vieweg, Braunschweig Wiesbaden, 2000. MR 1955795 (2003m:14002)
- 14.
- S. Iitaka, Algebraic Geometry: An Introduction to Birational Geometry of Algebraic Varieties, Graduate Texts in Math. 76, Springer-Verlag, New York, Heidelberg, Berlin, 1982. MR 0637060 (84j:14001)
- 15.
- K. Kendig, Elementary Algebraic Geometry, Graduate Texts in Math. 44, Springer-Verlag, New York, Heidelberg, Berlin, 1977. MR 0447222 (56:5537)
- 16.
- M. Kreuzer and L. Robbiano, Computational Commutative Algebra 1, Springer-Verlag, New York, Heidelberg, Berlin, 2000. MR 1790326 (2001j:13027)
- 17.
- Macaulay 2, available at http://www.math.uiuc.edu/Macaulay2/.
- 18.
- D. Mumford, Algebraic Geometry 1: Complex Projective Varieties, Grundlehren der mathematischen Wissenschaften 221, Springer-Verlag, New York, Heidelberg, Berlin, 1976. MR 1344216 (96d:14001)
- 19.
- D. Mumford, The Red Book of Varieties and Schemes, Lectures Notes in Math. 1358, Springer-Verlag, New York, Heidelberg, Berlin, 1999. MR 1748380 (2001b:14001)
- 20.
- M. Reid, Undergraduate Algebraic Geometry, London Mathematical Society Student Texts 12, Cambridge Univ. Press, Cambridge, 1988. MR 0982494 (90a:14001)
- 21.
- I. R. Shafarevich, Basic Algebraic Geometry, Grundlehren der mathematischen Wissenschaften 213, Springer-Verlag, New York, Heidelberg, Berlin, 1974. MR 0366917 (51:3163)
- 22.
- SINGULAR, available at http://www.singular.uni-kl.de/.
- 23.
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- 24.
- K. Ueno, Algebraic Geometry 1, 2, and 3, Trans. Math. Mono. 185, 197, and 218, AMS, Providence, 1999, 2001, and 2003. Translation of Diasu Kika, Iwanami Shoten, Tokyo, 1977. MR 1714917 (2000g:14001); MR 1810311 (2001j:14001); MR 1989998 (2004g:14001)
Additional Information:
Reviewer(s):
David
A.
Cox
Affiliation:
Amherst College
Email:
dac@cs.amherst.edu
Review Information:
Journal:
Bull. Amer. Math. Soc.
42
(2005),
113-118.
MSC
(2000):
Primary 14-01;
Secondary 13Pxx, 14Qxx
PII:
S 0273-0979(04)01038-9
Posted:
October 5, 2004
Copyright of article:
Copyright
2004,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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