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Desingularization by blowings-up avoiding simple normal crossings


Authors: Edward Bierstone, Sergio Da Silva, Pierre D. Milman and Franklin Vera Pacheco
Journal: Proc. Amer. Math. Soc. 142 (2014), 4099-4111
MSC (2010): Primary 14E15, 14J17, 32S45; Secondary 14B05, 32S05, 32S10
Published electronically: August 18, 2014
MathSciNet review: 3266981
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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.


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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

DOI: https://doi.org/10.1090/S0002-9939-2014-12178-2
Keywords: Resolution of singularities, simple normal crossings, desingularization invariant
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
Article copyright: © Copyright 2014 American Mathematical Society