Introduction to algebraic geometry

Introduction to Algebraic Geometry

Volumn , Issue , 2007, Pages 1-252

  Hassett, Brendan ^a  

^a RICE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84924517433     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1017/CBO9780511755224     Document Type: Book

References (39)

1. Michael Artin. Algebra. Englewood Cliffs, NJ: Prentice Hall Inc., 1991.
2. Hyman Bass. A nontriangular action of Ga on A3. J. Pure Appl. Algebra, 33:3(1984),1–5.
3. Etienne Bézout. General Theory of Algebraic Equations. Princeton, NJ: Princeton University Press, 2006. [Translated from the 1779 French original by Eric Feron.]
4. W. Dale Brownawell. Bounds for the degrees in the Nullstellensatz. Ann. Math. (2), 126:3(1987), 577–591.
5. Bruno Buchberger. Ein Algorithmus zum Auffinden der Basiselemente des Restklassenrings nach einem nulldimensionalen Polynomideal. PhD thesis, Universität Innsbruck, 1966.
6. Arthur Cayley. On the theory of elimination. Cambridge and Dublin Math. Journal, 3(1848),116–120. [Reprinted in Vol. 1 of the Collected Papers, Cambridge University Press, 1889; also reprinted in [12].]
7. C. Christensen, G. Sundaram, A. Sathaye, and C. Bajaj, eds. Algebra, Arithmetic and Geometry with Applications. Berlin: Springer-Verlag, 2004. [Papers from Shreeram S. Abhyankar’s 70th birthday conference held at Purdue University, West Lafayette, IN, July 20–26, 2000.]
8. David Cox, John Little, and Donal O’Shea. Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra. Undergraduate Texts in Mathematics. New York: Springer-Verlag, second edition, 1997.
9. David Eisenbud. Commutative Algebra: With a View Toward Algebraic Geometry. Graduate Texts in Mathematics, 150. New York: Springer-Verlag, 1995.
10. David Eisenbud, Craig Huneke, and Wolmer Vasconcelos. Direct methods for primary decomposition. Invent. Math., 110:2(1992), 207–235.
11. William Fulton. Algebraic Curves: An Introduction to Algebraic Geometry. Advanced Book Program. Redwood City, CA: Addison-Wesley, 1989. [Notes written with the collaboration of Richard Weiss, Reprint of 1969 original.]
12. I. M. Gelf and, M. M. Kapranov, and A. V. Zelevinsky. Discriminants, Resultants, and Multidimensional Determinants. Mathematics: Theory & Applications. Boston, MA: Birkhäuser Boston Inc., 1994.
13. Hermann Grassmann. A New Branch of Mathematics. Chicago, IL: Open Court Publishing Co., 1995. [The Ausdehnungslehre of 1844 and other works, translated from the German and with a note by Lloyd C. Kannenberg, With a foreword by Albert C. Lewis.]
14. Phillip Griffiths and Joseph Harris. Principles of Algebraic Geometry. New York: Wiley-Interscience, 1978. [Pure and applied mathematics.]
15. Brian Harbourne. The geometry of rational surfaces and Hilbert functions of points in the plane. In Proceedings of the 1984 Vancouver Conference in Algebraic Geometry, Vol. 6, ed. A. V. Geramita and P. Russell. Providence, RI: American Mathematical Society, 1986, pp. 95–111.
16. Brian Harbourne. Points in good position in P2. In Zero-Dimensional Schemes: Proceedings of the International Conference Held in Ravello, Italy, June 8–13, 1992, ed. F. Orecchia and L. Chiantini. Berlin: de Gruyter, 1994, pp. 213–229.
17. Joe Harris. Algebraic Geometry: A First Course. Graduate Texts in Mathematics, 133. New York: Springer-Verlag, 1992.
18. Joe Harris, Barry Mazur, and Rahul Pandharipande. Hypersurfaces of low degree. Duke Math. J., 95:1(1998), 125–160.
19. Robin Hartshorne. Algebraic Geometry. Graduate Texts in Mathematics, 52. New York: Springer-Verlag, 1977.
20. Brendan Hassett. Some rational cubic fourfolds. J. Algebraic Geom., 8:1(1999), 103–114.
21. André Hirschowitz. Une conjecture pour la cohomologie des diviseurs sur les surfaces rationnelles génériques. J. Reine Angew. Math., 397(1989), 208–213.
22. W. V. D. Hodge and D. Pedoe. Methods of Algebraic Geometry, Vol. I. Cambridge University Press, 1947.
23. Amit Khetan. The resultant of an unmixed bivariate system. J. Symbolic Comput., 36:3-4(2003), 425–442. [International Symposium on Symbolic and Algebraic Computation (ISSAC’2002) (Lille).]
24. János Kollár. Sharp effective Nullstellensatz. J. Am. Math. Soc., 1:4(1988), 963–975.
25. János Kollár. Low degree polynomial equations: arithmetic, geometry and topology. In European Congress of Mathematics, Vol. 1 (Budapest, 1996), ed. A. Balog, G. O. H. Katona, A. Recski and D. Szász. Progress in Mathematics, 168. Basel: Birkhäuser, 1998, pp. 255–288.
26. János Kollár. Unirationality of cubic hypersurfaces. J. Inst. Math. Jussieu, 1:3(2002), 467–476.
27. Serge Lang. Algebra, second edition. Advanced Book Program, Reading, MA: Addison-Wesley, 1984.
28. F. S. Macaulay. On some formula in elimination. Proc. Lond. Math. Soc., 3(1902), 3–27.
29. Hideyuki Matsumura. Commutative ring theory, Cambridge Studies in Advanced Mathematics, 8, second edition. Cambridge University Press, 1989. [Translated from the Japanese by M. Reid.]
30. Rick Miranda. Algebraic Curves and Riemann Surfaces, Graduate Studies in Mathematics, 5. Providence, RI: American Mathematical Society, 1995.
31. Rick Miranda. Linear systems of plane curves. Not. Am. Math. Soc., 46:2(1999), 192–201.
32. David Mumford. Lectures on Curves on an Algebraic Surface. [With a section by G. M. Bergman.] Annals of Mathematics Studies, 59. Princeton, NJ: Princeton University Press, 1966.
33. Emmy Noether. Idealtheorie in Ringbereichen. Math. Ann., 83(1921), 24–66.
34. Kapil H. Paranjape and V. Srinivas. Unirationality of the general complete intersection of small multidegree. In Flips and Abundance for Algebraic Threefolds. Paris: Société Mathématique de France, 1992, pages 241–248. [Papers from the Second Summer Seminar on Algebraic Geometry held at the University of Utah, Salt Lake City, Utah, August 1991, Astérisque No. 211 (1992).]
35. G. C. M. Ruitenburg. Invariant ideals of polynomial algebras with multiplicity free group action. Compositio Math., 71:2(1989), 181–227.
36. Frank Olaf Schreyer. Die Berechnung von Syzygien mit dem verallgemeinerten Weierstrass’schen Divisionssatz, 1980. Diploma thesis.
37. Igor R. Shafarevich. Basic Algebraic Geometry 1: Varieties in Projective Space, second edition. Berlin: Springer-Verlag, 1994. [Translated from the 1988 Russian edition and with notes by Miles Reid.]
38. Igor R. Shafarevich. Basic Algebraic Geometry 2: Schemes and Complex Manifolds, second edition. Berlin: Springer-Verlag, 1994. [Translated from the 1988 Russian edition by Miles Reid.]
39. B. L. van der Waerden. Moderne Algebra, Unter Benutzung von Vorlesungen von E. Artin und E. Noether I, II. Die Grundlehren der mathematischenWissenschaften in Einzeldarstellungen mit besonderer Ber¨ucksichtigung der Anwendungsgebiete Bd.33, 44. Berlin: J. Springer, 1930/1931. [1937, 1940 (second edition); Berlin-Göttingen-Heidelberg: Springer-Verlag, 1950, 1955 (third edition); 1955, 1959 (fourth edition); 1960 (fifth edition of vol. I); 1964 (sixth edition of vol. I); 1967 (seventh edition of vol. I); 1967 (fifth edition of vol. II); 1971 (eighth edition of vol. I). English translations: Frederick Ungar Publishing Co., New York, 1949 (second edition); Frederick Ungar Publishing Co., New York, 1970 (seventh edition of volume I and fifth edition of volume II); Springer-Verlag, New York, 1991; Springer-Verlag, New York, 2003.