Logarithmic pair

In algebraic geometry, a logarithmic pair consists of a variety, together with a divisor along which one allows mild logarithmic singularities.

Definition

A boundary Q-divisor on a variety is a Q-divisor D of the form Σd_iD_i where the D_i are the distinct irreducible components of D and all coefficients are rational numbers with 0≤d_i≤1.

A logarithmic pair (X,D) is a pair consisting of a normal variety X and a boundary Q-divisor D.

References

• Matsuki, Kenji (2002), Introduction to the Mori program, Universitext, Berlin, New York: Springer-Verlag, ISBN 978-0-387-98465-0, MR1875410