Basic properties of log canonical centers
We present the elementary properties of log canonical centers of log varieties.
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arXiv subjects
Florin Ambro
Publications and source records attributed to Florin Ambro.
The set of toric minimal log discrepancies
We describe the set of minimal log discrepancies of toric log varities, and study its accumulation points.
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Asymptotically saturated toric algebras
We show the finite generation of certain invariant graded algebras defined on toric weak log Fano fibrations. These are the toric version of FGA algebras, recently introduced by Shokurov in connections to the existence of flips.
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The nef dimension of log minimal models
This is a resume of the talk delivered at the Symposium on Hodge theory, Degeneration and Complex surfaces, Tagajo, Miyagi, March 2004.
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A semiampleness criterion
We give a criterion for a real divisor to be rational and semiample.
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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.
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Nef dimension of minimal models
We reduce the Abundance Conjecture in dimension 4 to the following numerical statement: if the canonical divisor K is nef and has maximal nef dimension, then K is big. From this point of view, we ``classify'' in dimension 2 nef divisors which have maximal nef dimension, but which are not big.
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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 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.
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Quasi-log varieties
We extend the Cone Theorem of the Log Minimal Model Program to log varieties with arbitrary singularities.
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Inversion of adjunction for non-degenerate hypersurfaces
We prove a precise inversion of adjunction formula for the log pair associated to a non-degenerate hypersurface. As a corollary, the minimal log discrepancies of non-degenerate normal hypersurface singularities are bounded from above by dimension.
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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-continuous function. We check this lower semi-continuity behaviour for varieties of dimension at most 3 and for toric varieties of arbitrary dimension.
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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. As an application, we simplify Kollár's proof for the Anghern and Siu's quadratic bound in the Fujita's Conjecture. We also connect adjunction and its precise inverse to the problem of building isolated log canonical singularities.
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Ladders on Fano varieties
We prove the existence of Fano ladders on weak log Fano varieties of coindex less than 4, as an application of adjunction and nonvanishing.
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The locus of log canonical singularities
The LCS locus is an essential ingredient in the proof of fundamental results of Log Minimal Model Program, such as nonvanishing and base point freeness theorems. We prove in this paper that the LCS locus of a log canonical variety has seminormal singularities.
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