10.4 Semi-log resolutions
The aim of this section is to discuss resolution theorems that are useful in the study of semi-log canonical varieties.
The basic existence result on resolutions was established by Hironaka (1964). We also need a strengthening of it, due to Szabó (1994), see also Bierstone and Milman (1997, section 12).
Theorem 10.45 (Existence of log resolutions) Let X be a scheme or an algebraic space of finite type over a field of characteristic 0 and D a Weil divisor on X.
(1) Hironaka (1964)
) has a log resolution
(2) Szabó (1994); Bierstone and Milman (1997)
) has a log resolution f: X′ → X such that f is an isomorphism over the snc locus of
Corollary 10.46 (Resolution in families) Let C be a ...