A log resolution of a pair 
is a proper birational
morphism 
from a smooth variety for which the strict transform
of the support of 
and the exceptional divisors of 
together have simple normal crossing support. The morphism
is required to be an isomorphism over the locus where
the pair already has this form. The transformed boundary is not just the pullback
divisor, since exceptional components also enter discrepancy computations. Log resolutions
allow log discrepancies to be computed on smooth
models (Kollár and Mori 1998).
Log Resolution
See also
Divisorial Log Terminal Pair, Log Discrepancy, Resolution of Singularities, Simple Normal Crossing DivisorExplore with Wolfram|Alpha
References
Kollár, J. and Mori, S. Birational Geometry of Algebraic Varieties. Cambridge, England: Cambridge University Press, 1998. https://doi.org/10.1017/CBO9780511662560.Cite this as:
Weisstein, Eric W. "Log Resolution." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/LogResolution.html