Logarithmic pair
In algebraic geometry, a logarithmic pair consists of a variety, together with a divisor along which one allows mild logarithmic singularities. They were studied by.
Definition
A boundary Q-divisor on a variety is a Q-divisor D of the form ΣdiDi where the Di are the distinct irreducible components of D and all coefficients are rational numbers with 0≤di≤1.A logarithmic pair, or log pair for short, is a pair consisting of a normal variety X and a boundary Q-divisor D.
The log canonical divisor of a log pair is K+''D where K'' is the canonical divisor of X.
A logarithmic 1-form on a log pair is allowed to have logarithmic singularities of the form
d log = dz/''z along components of the divisor given locally by z''=0.