A note on the fiber dimension theorem
DOI:
https://doi.org/10.4067/S0716-09172009000100006Keywords:
Fiber dimension theorem, Non-closed points.Abstract
The aim of this work is to prove a version of the Fiber Dimension Theorem, emphasizing the case of non-closed points.
Resumo
El objetivo de este trabajo es probar una versión del Teorema de la Dimensión de la Fibra, enfatizando el caso de puntos no cerrados.
References
[1] M. F. Atiyah & I. G. Macdonald, Introduction to Commutative Algebra, Addison-Wesley, Reading, MA, (1969).
[2] D. Avritzer & I. Vainsencher, Hilb4P2, Lecture Notes in Mathematics, 1436, Springer Verlag, pp. 30-59, (1990).
[3] A. Beauville, Complex Algebraic Surfaces, Ast´erisque 54, pp. 63- 66, (1978).
[4] B. Crauder & R. Miranda, Quantum Cohomology of Rational Surfaces, In: The Moduli Space of Curves, Edited by R. Dijkgraaf, C. Faber, and G. van der Geer. Birhauser Press, Boston, pp. 35-82, (1995).
[5] I. Dolgachev, Introduction to Algebraic Geometry , http://www.math.lsa.umich.edu/~idolga/lecturenotes.html.
[6] D. Eisenbud, Commutative Algebra with a View Toward Algebraic Geometry, Graduate Texts in Math. 150, Springer, New York, (1995).
[7] B. Harbourne, Problems and Progress: A survey on fat points in P2, Queen’s papers in Pure and Applied Mathematics, The Curves Seminar at Queen’s, vol. 123, (2002).
[8] J. Harris, Algebraic Geometry: A first course, Graduate Texts in Math. 133, Springer, New York, (1995).
[9] J. Harris & D. Eisenbud, The Geometry of Schemes, Graduate Texts in Math. 197, Springer, New York, (1999).
[10] R. Hartshorne, Algebraic Geometry, Graduate Texts in Math. 52, Springer, New York, (1977).
[11] D. Mumford, The Red Book of Varieties and Schemes, Lecture Notes in Math. 1358, Springer, Berlin, (1988).
[12] M. Reid, Undergraduate Algebraic Geometry, London Mathematical Society Students Texts 12, Cambridge University Press, Cambridge and New York, (1988).
[13] J. Rojas & I. Vainsencher, Conical Sextuplets, Communications in Algebra, 24(11), pp. 3437-3457, (1996).
[2] D. Avritzer & I. Vainsencher, Hilb4P2, Lecture Notes in Mathematics, 1436, Springer Verlag, pp. 30-59, (1990).
[3] A. Beauville, Complex Algebraic Surfaces, Ast´erisque 54, pp. 63- 66, (1978).
[4] B. Crauder & R. Miranda, Quantum Cohomology of Rational Surfaces, In: The Moduli Space of Curves, Edited by R. Dijkgraaf, C. Faber, and G. van der Geer. Birhauser Press, Boston, pp. 35-82, (1995).
[5] I. Dolgachev, Introduction to Algebraic Geometry , http://www.math.lsa.umich.edu/~idolga/lecturenotes.html.
[6] D. Eisenbud, Commutative Algebra with a View Toward Algebraic Geometry, Graduate Texts in Math. 150, Springer, New York, (1995).
[7] B. Harbourne, Problems and Progress: A survey on fat points in P2, Queen’s papers in Pure and Applied Mathematics, The Curves Seminar at Queen’s, vol. 123, (2002).
[8] J. Harris, Algebraic Geometry: A first course, Graduate Texts in Math. 133, Springer, New York, (1995).
[9] J. Harris & D. Eisenbud, The Geometry of Schemes, Graduate Texts in Math. 197, Springer, New York, (1999).
[10] R. Hartshorne, Algebraic Geometry, Graduate Texts in Math. 52, Springer, New York, (1977).
[11] D. Mumford, The Red Book of Varieties and Schemes, Lecture Notes in Math. 1358, Springer, Berlin, (1988).
[12] M. Reid, Undergraduate Algebraic Geometry, London Mathematical Society Students Texts 12, Cambridge University Press, Cambridge and New York, (1988).
[13] J. Rojas & I. Vainsencher, Conical Sextuplets, Communications in Algebra, 24(11), pp. 3437-3457, (1996).
How to Cite
[1]
J. F. Rojas and R. Mendoza, “A note on the fiber dimension theorem”, Proyecciones (Antofagasta, On line), vol. 28, no. 1, pp. 57-73, 1.
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