Local monomialization and factorization of morphisms

Cutkosky, Steven Dale

Astérisque, no. 260 (1999) , 149 p.

MR Zbl | 4 citations dans Numdam

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     author = {Cutkosky, Steven Dale},
     title = {Local monomialization and factorization of morphisms},
     series = {Ast\'erisque},
     year = {1999},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {260},
     mrnumber = {1734239},
     zbl = {0941.14001},
     language = {en},
     url = {https://www.numdam.org/item/AST_1999__260__1_0/}
}

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%A Cutkosky, Steven Dale
%T Local monomialization and factorization of morphisms
%S Astérisque
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Cutkosky, Steven Dale. Local monomialization and factorization of morphisms. Astérisque, no. 260 (1999), 149 p. https://www.numdam.org/item/AST_1999__260__1_0/

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[1] Abhyankar, S., Local uniformization on algebraic surfaces over ground fields of characteristic $p \neq 0$ , Annals of Math., 63 (1956), 491-526. | MR | Zbl | DOI

[2] Abhyankar, S., On the valuations centered in a local domain, Amer. J. Math. 78 (1956), 321-348. | MR | Zbl | DOI

[3] Abhyankar, S., Ramification theoretic methods in algebraic geometry, Princeton University Press, 1959. | MR | Zbl | DOI

[4] Abhyankar, S., Resolution of singularities of embedded algebraic surfaces, Academic Press, New York, 1966. | MR | Zbl

[5] Abhyankar, S., Algebraic Geometry for Scientists and Engineers, American Mathematical Society, 1990. | MR | Zbl | DOI

[6] Abhyankar, S., Simultaneous resolution for algebraic surfaces, Amer. J. Math. 78 (1956), 761-790. | MR | Zbl | DOI

[7] Abramovich, D., Matsuki, K., Rashid, S., A note on the factorization theorem of toric birational maps after Morelli and its toroidal extension, preprint. | Zbl | MR | DOI

[8] Akbulut S and King, H, Topology of algebraic sets, MSRI publications 25, Springer-Verlag Berlin. | MR

[9] Cano, F. T., Desingularization strategies for three-dimensional vector fields, Lecture Notes in Math. 1259, Springer-Verlag, Heidelberg (1987). | MR | Zbl

[10] Christensen, C, Strong domination/weak factorization of three dimensional regular local rings, Journal of the Indian Math. Soc., 45 (1981), 21-47. | MR | Zbl

[11] Cossart, V., Polyèdre caractéristique d'une singularité, Thèse, Université de Paris-Sud, Centre d'Orsay (1987).

[12] Crauder, B., Birational morphisms of smooth algebraic $3$ -folds collapsing $3$ surfaces to a point, Duke Math. J. 48 (1981), 589-632. | Zbl | MR | DOI

[13] Cutkosky, S. D., Local Factorization of Birational Maps, Advances in Math. 132, (1997), 167-315. | MR | Zbl | DOI

[14] Cutkosky, S. D., Simultaneous resolution of singularities, to appear in Proc. AMS. | MR | Zbl

[15] Danilov, V. I., The decomposition of certain birational morphisms, Math. USSR Izv. 44 (1980), 465-477. | MR | Zbl

[16] Danilov, V. I., Birational geometry of toric varieties, Math USSR Izv. 21 (1983), 269-280. | Zbl | DOI

[17] Ewald, G., Blow-ups of smooth toric $3$ -varieties, Abh. Math. Sem. Univ. Hamburg 57 (1987), 193-201. | MR | Zbl | DOI

[18] Giraud, J., Condition de Jung pour les revêtements radiciels de hauteur un, Proc. Algebraic Geometry, Tokyo/Kyoto 1982. Lecture Notes in Math. 1016, Springer-Verlag (183) 313-333. | MR | Zbl

[19] Hartshorne, R., Algebraic Geometry, Springer, New York, Heidelberg, Berlin (1977). | MR | Zbl | DOI

[20] Hironaka, H., Resolution of singularities of an algebraic variety over a field of characteristic zero, Annals of Math., 79 (1964), 109-326. | MR | Zbl | DOI

[21] Hironaka, H., On the theory of birational blowing up, Thesis, Harvard (1960). | MR

[22] Heinzer, W., Huneke, H., Sally J., A criterion for spots, J. Math. Kyoto Univ. 26 (1986) 667-671. | MR | Zbl | DOI

[23] Heinzer, W. and Sally, J., Extensions of valuations to the completion of a local domain, Journal of pure and applied algebra 71 (1991), 175-185. | MR | Zbl | DOI

[24] Lipman, J., Appendix to chapter II of Zariski, O., Algebraic Surfaces, second edition, Springer Verlag, Berlin, (1971). | Zbl | MR

[25] Lipman, J., Desingularization of two-dimensional schemes, Annals of Math. 107 (1978), 151-207. | MR | Zbl | DOI

[26] Matsumura, H., Commutative Ring Theory, Cambridge University press, Cambridge (1986). | MR | Zbl

[27] Morelli, R., The birational geometry of toric varieties, J. Algebraic Geometry 5 (1996) 751-782. | MR | Zbl

[28] Nagata, M., Local Rings, Interscience tracts in Pure and Applied Math. 13, J. Wiley, New York (1962). | MR | Zbl

[29] Pinkham, H., Factorization of birational maps in dimension three, Proceedings of Symposia in Pure Mathematics, Vol. 40, Part 2, America Mathematical Society, Providence (1983), 343-372. | MR | Zbl | DOI

[30] Sally, J., Regular overrings of regular local rings, Trans. Amer. Math. Soc. 171 (1972) 291-300. | MR | Zbl | DOI

[31] Schilling, O., The theory of valuations, Amer. Math. Soc, 1950. | MR | Zbl | DOI

[32] Seidenberg, A., Reduction of the singularities of the differential equation $A d y = B d x$ , Amer. J. Math. 90 (1968), 248-269. | Zbl | MR | DOI

[33] Shannon, D. L., Monodial transforms, Amer. J. Math., 45 (1973), 284-320.

[34] Wlodarczyk J., Decomposition of birational toric maps in blowups and blowdowns. Trans. Amer. Math. Soc. 349 (1997), 373-411. | MR | Zbl | DOI

[35] Zariski, O., The reduction of the singularities of an algebraic surface, Annals of Math., 40 (1939) 639-689. | MR | Zbl | DOI

[36] Zariski, O., Local uniformization of algebraic varieties, Annals of Math., 41, (1940), 852-896. | MR | Zbl | JFM | DOI

[37] Zariski, O., Reduction of the singularities of algebraic three dimensional varieties, Annals of Math., 45 (1944) 472-542. | MR | Zbl | DOI

[38] Zariski, O., Introduction to the problem of minimal models in the theory of algebraic surfaces, Publications of the math. Soc. of Japan, (1958). | MR | Zbl

[39] Zariski, O. and Samuel, P., Commutative Algebra II, Van Nostrand, Princeton (1960). | MR | Zbl