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Quasi-log varieties
We extend the Cone Theorem of the Log Minimal Model Program to log varieties with arbitrary singularities.
Ladders on Fano varieties
We prove the existence of ladders on log Fano varieties of coindex less than 4, as an application of adjunction and nonvanishing.
The Adjunction Conjecture and its applications
We discuss adjunction formulas for fiber spaces and embeddings, extending the known results along the lines of the Adjunction Conjecture, independently proposed by Y. Kawamata and V.V. Shokurov. AsExpand
Shokurov's Boundary Property
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 oneExpand
On minimal log discrepancies
An explanation to the boundness of minimal log discrepancies conjectured by V.V. Shokurov would be that the minimal log discrepancies of a variety in its closed points define a lower semi-continuousExpand
The moduli b-divisor of an lc-trivial fibration
We study positivity properties of the moduli (b-)divisor associated to a relative log pair (X, B)/Y with relatively trivial log canonical class.
Variation of log canonical thresholds in linear systems
We investigate the variation of log canonical thresholds in (graded) linear systems. For toric log Fano varieties, we give a sharp lower bound for log canonical thresholds of the anticanonicalExpand
An injectivity theorem
  • Florin Ambro
  • Mathematics
  • Compositio Mathematica
  • 27 September 2012
Abstract We generalize the injectivity theorem of Esnault and Viehweg, and apply it to the structure of log canonical type divisors.
On the classification of toric singularities
For a toric log variety with standard coefficients, we show that the minimal log discrepancy at a closed invariant point bounds the Cartier index of a neighbourhood.
Minimal models of semi-log-canonical pairs
We compare the minimal model of a log canonical pair with the minimal model of its reduced boundary. These results are then used to study the existence of the minimal model of a semi-log-canonicalExpand