Book Review
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Book Information:
Author:
H. Schenck
Title:
Computational algebraic geometry
Additional book information:
London Mathematical Society Student Texts, vol. 58,
Cambridge University Press, Cambridge,
2003,
xiv+ 193 pp.,
ISBN 0-521-82964-X,
$70.00$,
hardback;
ISBN 0-521-53650-2,
$28.00$,
paperback
William W. Adams and Philippe Loustaunau, An introduction to Gröbner bases, Graduate Studies in Mathematics, vol. 3, American Mathematical Society, Providence, RI, 1994. MR 1287608, DOI 10.1090/gsm/003
Thomas Becker and Volker Weispfenning, Gröbner bases, Graduate Texts in Mathematics, vol. 141, Springer-Verlag, New York, 1993. A computational approach to commutative algebra; In cooperation with Heinz Kredel. MR 1213453, DOI 10.1007/978-1-4612-0913-3
3. CoCoA, available at http://cocoa.dima.unige.it/.
David Cox, John Little, and Donal O’Shea, Ideals, varieties, and algorithms, 2nd ed., Undergraduate Texts in Mathematics, Springer-Verlag, New York, 1997. An introduction to computational algebraic geometry and commutative algebra. MR 1417938
David Eisenbud, Commutative algebra, Graduate Texts in Mathematics, vol. 150, Springer-Verlag, New York, 1995. With a view toward algebraic geometry. MR 1322960, DOI 10.1007/978-1-4612-5350-1
David Eisenbud and Joe Harris, The geometry of schemes, Graduate Texts in Mathematics, vol. 197, Springer-Verlag, New York, 2000. MR 1730819
David Eisenbud, Daniel R. Grayson, Michael Stillman, and Bernd Sturmfels (eds.), Computations in algebraic geometry with Macaulay 2, Algorithms and Computation in Mathematics, vol. 8, Springer-Verlag, Berlin, 2002. MR 1949544, DOI 10.1007/978-3-662-04851-1
Gert-Martin Greuel and Gerhard Pfister, A Singular introduction to commutative algebra, Springer-Verlag, Berlin, 2002. With contributions by Olaf Bachmann, Christoph Lossen and Hans Schönemann; With 1 CD-ROM (Windows, Macintosh, and UNIX). MR 1930604, DOI 10.1007/978-3-662-04963-1
Phillip Griffiths and Joseph Harris, Principles of algebraic geometry, Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons], New York, 1978. MR 507725
A. Grothendieck, Éléments de géométrie algébrique. I. Le langage des schémas, Inst. Hautes Études Sci. Publ. Math. 4 (1960), 228 (French). MR 217083
Joe Harris, Algebraic geometry, Graduate Texts in Mathematics, vol. 133, Springer-Verlag, New York, 1992. A first course. MR 1182558, DOI 10.1007/978-1-4757-2189-8
Robin Hartshorne, Algebraic geometry, Graduate Texts in Mathematics, No. 52, Springer-Verlag, New York-Heidelberg, 1977. MR 0463157
Klaus Hulek, Elementary algebraic geometry, Student Mathematical Library, vol. 20, American Mathematical Society, Providence, RI, 2003. Translated from the 2000 German original by Helena Verrill. MR 1955795, DOI 10.1090/stml/020
Shigeru Iitaka, Algebraic geometry, North-Holland Mathematical Library, vol. 24, Springer-Verlag, New York-Berlin, 1982. An introduction to birational geometry of algebraic varieties. MR 637060
Keith Kendig, Elementary algebraic geometry, Graduate Texts in Mathematics, No. 44, Springer-Verlag, New York-Berlin, 1977. MR 0447222
Martin Kreuzer and Lorenzo Robbiano, Computational commutative algebra. 1, Springer-Verlag, Berlin, 2000. MR 1790326, DOI 10.1007/978-3-540-70628-1
17. Macaulay 2, available at http://www.math.uiuc.edu/Macaulay2/.
David Mumford, Algebraic geometry. I, Classics in Mathematics, Springer-Verlag, Berlin, 1995. Complex projective varieties; Reprint of the 1976 edition. MR 1344216
David Mumford, The red book of varieties and schemes, Second, expanded edition, Lecture Notes in Mathematics, vol. 1358, Springer-Verlag, Berlin, 1999. Includes the Michigan lectures (1974) on curves and their Jacobians; With contributions by Enrico Arbarello. MR 1748380, DOI 10.1007/b62130
Miles Reid, Undergraduate algebraic geometry, London Mathematical Society Student Texts, vol. 12, Cambridge University Press, Cambridge, 1988. MR 982494, DOI 10.1017/CBO9781139163699
I. R. Shafarevich, Basic algebraic geometry, Die Grundlehren der mathematischen Wissenschaften, Band 213, Springer-Verlag, New York-Heidelberg, 1974. Translated from the Russian by K. A. Hirsch. MR 0366917
22. SINGULAR, available at http://www.singular.uni-kl.de/.
Karen E. Smith, Lauri Kahanpää, Pekka Kekäläinen, and William Traves, An invitation to algebraic geometry, Universitext, Springer-Verlag, New York, 2000. MR 1788561, DOI 10.1007/978-1-4757-4497-2
Kenji Ueno, Algebraic geometry. 1, Translations of Mathematical Monographs, vol. 185, American Mathematical Society, Providence, RI, 1999. From algebraic varieties to schemes; Translated from the 1997 Japanese original by Goro Kato; Iwanami Series in Modern Mathematics. MR 1714917, DOI 10.1090/mmono/185
- 1.
- W. Adams and P. Loustaunau, An Introduction to Gröbner Bases, Graduate Studies in Math. 3, AMS, Providence, 1994. MR 1287608
- 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
- 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
- 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
- 6.
- D. Eisenbud and J. Harris, The Geometry of Schemes, Graduate Texts in Math. 197, Springer-Verlag, New York, Heidelberg, Berlin, 2002. MR 1730819
- 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
- 8.
- G.-M. Greuel and G. Pfister, A Singular Introduction to Commutative Algebra, Springer-Verlag, New York, Heidelberg, Berlin, 2002. MR 1930604
- 9.
- P. Griffiths and J. Harris, Principles of Algebraic Geometry, Series in Pure & Applied Mathematics, Wiley, New York, 1978. MR 0507725
- 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; MR 0163909 (29:1208); MR 0163910 (29:1209); MR 0163911; MR 0173675 (30:3885); MR 0199181 (33:7330); MR 0217086; MR 0238860 (39:220)
- 11.
- J. Harris, Algebraic Geometry, Graduate Texts in Math. 133, Springer-Verlag, New York, Heidelberg, Berlin, 1992. MR 1182558
- 12.
- R. Hartshorne, Algebraic Geometry, Graduate Texts in Math. 52, Springer-Verlag, New York, Heidelberg, Berlin, 1977. MR 0463157
- 13.
- K. Hulek, Elementary Algebraic Geometry, Student Mathematical Library 20, AMS, Providence, 2003. Translation of Elementare Algebraische Geometrie, Vieweg, Braunschweig Wiesbaden, 2000. MR 1955795
- 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
- 15.
- K. Kendig, Elementary Algebraic Geometry, Graduate Texts in Math. 44, Springer-Verlag, New York, Heidelberg, Berlin, 1977. MR 0447222
- 16.
- M. Kreuzer and L. Robbiano, Computational Commutative Algebra 1, Springer-Verlag, New York, Heidelberg, Berlin, 2000. MR 1790326
- 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
- 19.
- D. Mumford, The Red Book of Varieties and Schemes, Lectures Notes in Math. 1358, Springer-Verlag, New York, Heidelberg, Berlin, 1999. MR 1748380
- 20.
- M. Reid, Undergraduate Algebraic Geometry, London Mathematical Society Student Texts 12, Cambridge Univ. Press, Cambridge, 1988. MR 0982494
- 21.
- I. R. Shafarevich, Basic Algebraic Geometry, Grundlehren der mathematischen Wissenschaften 213, Springer-Verlag, New York, Heidelberg, Berlin, 1974. MR 0366917
- 22.
- SINGULAR, available at http://www.singular.uni-kl.de/.
- 23.
- K. Smith, L. Kahanpää, P. Kekäläinen, and W. Traves, An Invitation to Algebraic Geometry, Universitext, Springer-Verlag, New York, Heidelberg, Berlin, 2000. MR 1788561
- 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; MR 1810311 (2001j:14001); MR 1989998
Review Information:
Reviewer:
David A. Cox
Affiliation:
Amherst College
Email:
dac@cs.amherst.edu
Journal:
Bull. Amer. Math. Soc.
42 (2005), 113-118
Published electronically:
October 5, 2004
Review copyright:
© Copyright 2004
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
