Shokurov's Boundary Property

By Florin Ambro. 2002

132 citations recorded by the source corpus.

For a birational analogue of minimal elliptic surfaces X/Y, the singularities of the fibers define a log structure in codimension one on Y. Via base change, we have a log structure 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). We have three applications: inverse of adjunction for the above mentioned fiber spaces, the invariance of Shokurov's FGA-algebras under restriction to exceptional lc centers, and a remark on the moduli part of parabolic fiber spaces.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/38c1a53fa0f803b5619b629c6d382393ad602eb2

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Existence of log canonical closures (2011, methodology): “[Ambro04] F. Ambro, Shokurov’s boundary property.”
Burniat surfaces I: fundamental groups and moduli of primary Burniat surfaces (2009, methodology): “and (3), Ambro’s theorem (see [A1, Theorems 0.2 and 2.7] or Theorem 3.2) holds if we use [N3, 3.7. Theorem (4)] in the proof of Ambro’s theorem. Note that it is not diﬃcult to modify the arguments in [A1] for our setting. More explicitly, let σ : Z′ →Z be a proper birational morphism from a normal p”
On a generalized canonical bundle formula and generalized adjunction (2018, methodology): “By the classic theory of adjunction for fiber spaces [2, 29, 17], it induces bdivisors BZ′ and M A Z on Z .”