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Simultaneous resolution of singularities
Author(s):
Steven
Dale
Cutkosky
Journal:
Proc. Amer. Math. Soc.
128
(2000),
1905-1910.
MSC (1991):
Primary 13B15, 14B05
Posted:
November 24, 1999
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Abstract:
We prove a local theorem on simultaneous resolution of singularities, which is valid in all dimensions. This theorem is proven in dimension 2 (and in all characteristics) by Abhyankar in his book ``Ramification theoretic methods in algebraic geometry'' (1959).
References:
- 1.
- Abhyankar, S., Local uniformization on algebraic surfaces over ground fields of characteristic
 , Annals of Math, 63 (1956), 491-526. MR 17:1134d - 2.
- Abhyankar, S., Ramification theoretic methods in algebraic geometry, Princeton University Press, 1959. MR 21:4158
- 3.
- Abhyankar, S., Resolution of singularities of embedded algebraic surfaces, Academic Press, New York, 1966. MR 36:164
- 4.
- Abhyankar, S., Simultaneous resolution for algebraic surfaces, Amer. J. Math 78 (1956), 761-790. MR 18:600b
- 5.
- Cutkosky, S.D., Local factorization of birational maps, Advances in Math. 132, (1997), 167-315. MR 99c:14018
- 6.
- Cutkosky, S.D., Local factorization and monomialization of morphisms, to appear in Astérisque.
- 7.
- Fu, D., Local weak simultaneous resolution for high rational ranks, J. Algebra 194 (1997), 614-630. MR 98m:13005
- 8.
- Hironaka, H., Resolution of singularities of an algebraic variety over a field of characteristic zero, Annals of Math, 79 (1964), 109-326. MR 33:7333
- 9.
- Matsumura, H, Commutative Algebra, second edition, Benjamin/Cummings, Reading Mass, 1980. MR 82i:13003
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Additional Information:
Steven
Dale
Cutkosky
Affiliation:
Department of Mathematics, University of Missouri, Columbia, Missouri 65211
Email:
dale@cutkosky.math.missouri.edu
DOI:
10.1090/S0002-9939-99-05191-6
PII:
S 0002-9939(99)05191-6
Received by editor(s):
April 27, 1998
Received by editor(s) in revised form:
August 24, 1998
Posted:
November 24, 1999
Additional Notes:
The author was partially supported by NSF
Communicated by:
Wolmer V. Vasconcelos
Copyright of article:
Copyright
2000,
American Mathematical Society
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