# Birational model of a log smooth pair

Given a log smooth pair $$(X,B)$$ with a reduced boundary divisor $$B$$, consider a birational model $$\pi:X' \to X$$ and a boundary divisor $$B'$$ which is given by $$K_{X'}+B'=\pi^*(K_X+B)$$. Here is my question:

(1) can we construct an example that $$(X',B')$$ is not sub-dlt?

(2) is there an lc center of $$(X',B')$$ which is not an irreducible component of an intersection locus of some certain components of $$B'^{=1}$$ (this means the coefficient one part of $$B'$$)?

• What about $\mathbb{A}^2$ with the two lines, and then you blow-up $(x,y^n)$? So I think the answer to the first one is yes. The second answer should be no, the morphism $X'\rightarrow X$ should be toroidal around the divisors with coefficient one. Feb 17, 2020 at 17:54
• The second answer should be no, the morphism $X′\to X$ should be toroidal around the divisors with coefficient one. Thank you! This is exactly what I need. Could you please offer a reference or something? The term "toroidal" is really confusing to me.. Feb 18, 2020 at 2:28