dlt modification

PROPOSITION 2.2.3 Let .X; / be a log pair where X is a variety and the coefficients of belong to Œ0; 1 . Then there is a projective birational morphism W Y ! X such that (1) Y is Q-factorial, (2) only extracts divisors of log discrepancy at most 0, (3) if E D P Ei is the sum of the -exceptional divisors and is the strict transform of , then .Y; C E/ is divisorially log terminal and KY C E C D .KX C / C X a.Ei ;X;B/<0 a.Ei ; X; B/Ei : Any birational morphism W Y ! X satisfying (1)–(3) is called a divisorially log terminal modification. (paper) (Brown et al., 2018, p. 933)