Desingularization by blowings-up avoiding simple normal crossings
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- by Edward Bierstone, Sergio Da Silva, Pierre D. Milman and Franklin Vera Pacheco PDF
- Proc. Amer. Math. Soc. 142 (2014), 4099-4111 Request permission
Abstract:
It is shown that, for any reduced algebraic variety in characteristic zero, one can resolve all but simple normal crossings (snc) singularities by a finite sequence of blowings-up with smooth centres which, at every step, avoids points where the transformed variety together with the exceptional divisor has only snc singularities. The proof follows the philosophy of Bierstone and Milman’s Resolution except for minimal singularities I (2012) that the desingularization invariant can be used together with natural geometric information to compute local normal forms of singularities.References
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Additional Information
- Edward Bierstone
- Affiliation: The Fields Institute, 222 College Street, Toronto, Ontario, Canada M5T 3J1 – and – Department of Mathematics, University of Toronto, 40 St. George Street, Toronto, Ontario, Canada M5S 2E4
- Email: bierston@math.toronto.edu
- Sergio Da Silva
- Affiliation: Department of Mathematics, University of Toronto, 40 St. George Street, Toronto, Ontario, Canada M5S 2E4
- Address at time of publication: Department of Mathematics, Cornell University, 310 Malott Hall, Ithaca, New York 14853
- Email: smd322@cornell.edu
- Pierre D. Milman
- Affiliation: Department of Mathematics, University of Toronto, 40 St. George Street, Toronto, Ontario, Canada M5S 2E4
- Email: milman@math.toronto.edu
- Franklin Vera Pacheco
- Affiliation: The Fields Institute, 222 College Street, Toronto, Ontario, Canada M5T 3J1
- Email: franklin.vp@gmail.com
- Received by editor(s): July 18, 2012
- Received by editor(s) in revised form: February 4, 2013
- Published electronically: August 18, 2014
- Additional Notes: Research supported in part by NSERC grants OGP0009070, MRS342058, USRA191085, CGS145594585 and OGP0008949.
- Communicated by: Lev Borisov
- © Copyright 2014 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 142 (2014), 4099-4111
- MSC (2010): Primary 14E15, 14J17, 32S45; Secondary 14B05, 32S05, 32S10
- DOI: https://doi.org/10.1090/S0002-9939-2014-12178-2
- MathSciNet review: 3266981