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,B _Y ) in codimension one on Y. Via base change, we have a log structure (Y′,B _Y′) 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.