Shokurov’s boundary property

Abstract

For a birational analogue of minimal elliptic surfaces f : X → Y, the singularities of the fibers allow us to define a log structure (Y, BY) in codimension one on Y . Via base change, we have a log structure (Y′, BY′) in codimension one on Y′, for any birational model Y′ of Y . We show that these codimension one log structures glue to a unique log structure, defined on some birational model of Y (Shokurov’s BP Conjecture). As applications, we obtain Inversion of Adjunction for the above mentioned fiber spaces, and the invariance of Shokurov′s FGA-algebras under adjunction. © 2004 Applied Probability Trust.