Monomial resolutions of morphisms of algebraic surfaces

Communications in Algebra

Volumn 28, Issue 12, 2000, Pages 5935-5959

  Cutkosky, Dale ^a   Piltant, Olivier ^b  

^a UNIVERSITY OF MISSOURI   (United States)

^b ECOLE POLYTECHNIQUE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040182770     PISSN: 00927872     EISSN: None     Source Type: Journal    
DOI: 10.1080/00927870008827198     Document Type: Article

References (20)

1. ABHYANKAR S., On the valuations centered in a local domain, Amer. J. of Math. 78 (1956), 321-348.
2. ABHYANKAR S., Simultaneous resolution for algebraic surfaces, Amer. J. of Math. 78 (1956), 761-790.
3. ABHYANKAR S., Ramification theoretic methods in algebraic geometry, Annals of Math. Studies 43, Princeton University Press (1959).
4. ABHYANKAR S., Local Uniformization on algebraic surfaces over ground fields of characteristic p ≠ 0, Annals of Math. 63 (1956), 491-526.
5. ABHYANKAR S., Tame coverings and fundamental groups of algebraic varieties, Amer. J. Math. 81 (1959).
6. ABRAMOVICH D. AND KARU K., Weak semistable reduction in characteristic 0, preprint.
7. AKBULUT S. AND KING H., Topology of algebraic sets, MSRI publications 25, Springer Verlag (1992).
8. CUTKOSKY S.D., Local factorization and monomialization of morphisms, Astérisque, to appear.
9. GROTHENDIECK A. AND MURRE J.P., The tame fundamental group of a formal neighbourhood of a divisor with normal crossings on a scheme, Lect. Notes in Math. 208, Springer-Verlag (1971).
10. HARTSHORNE R., Algebraic geometry, Graduate Texts in Math. 52, Springer-Verlag (1977).
11. HIRONAKA H., Desingularization of excellent surfaces, in Cossart V., Giraud J. and Orbanz U., Resolution of singularities, Lect. Notes in Math. 1101, Springer-Verlag (1980).
12. KEMPF G., KNUDSEN F., MUMFORD D. AND SAINT-DONAT B., Toroidal embeddings I, Lect. Notes in Math. 339, Springer-Verlag (1973).
13. LIPMAN J., Rational singularities, with applications to algebraic surfaces and unique factorization, Publ. Math. IHES 36 (1969), 195-279.
14. LIPMAN J., Desingularization of 2-dimensional schemes, Annals of Math. 107 (1978), 115-207.
15. MILNE J.S., Etale cohomology, Princeton Series in Math. 33, Princeton University Press (1980).
16. GROTHENDIECK A., Revêtements étales et groupe fondemental, Lecture Notes in Math 224, Springer Verlag, Heidelberg (1971).
17. SPIVAKOVSKY M., Valuations in function fields of surfaces, Amer. J. of Math. 112 (1990), 107-156.
18. ZARISKI, O., Local uniformization of algebraic varieties, Annals of Math., 41, (1940), 852-896.
19. ZARISKI O. AND SAMUEL P., Commutive algebra I, Graduate Texts in Math. 28, Springer-Verlag (1958).
20. ZARISKI O. AND SAMUEL P., Commutive algebra II, The Univ. Series in Higher Math., Van Norstrand (1960).