Mld versus lct near zero
We study the equivalence of approaching zero for two invariants of a singularity: the minimal log discrepancy and the log canonical threshold of the general hyperplane section.
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arXiv subjects
Florin Ambro
Publications and source records attributed to Florin Ambro.
An explicit bound for complements on toric varieties
We give an effective upper bound for the index of klt complements on toric Fano varieties.
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Classification of toric surface singularities
We classify two-dimensional toric log germs in terms of their minimal log discrepancy.
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Successive vanishing on curves
We investigate the emptiness of adjoint linear systems associated to successive multiples of a given positive divisor with real coefficients
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On toric Fano fibrations
A. Borisov classified into finitely many series the set of isomorphism classes of germs of toric $\Q$-factorial singularities, of fixed dimension and with minimal log discrepancy over the special point bounded from below by a fixed real number. We extend this classification to germs of toric Fano fibrations, possibly not $\Q$-factorial. As an application, we verify in the toric setting a conjecture proposed by V. V. Shokurov on the existence of bounded complements.
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Positivity of the Moduli Part
We prove the Cone Theorem for algebraically integrable foliations. As a consequence, we show that termination of flips implies the b-nefness of the moduli part of a log canonical pair with respect to a contraction, generalising the case of lc trivial fibrations.
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Successive minima of line bundles
We introduce and study the successive minima of line bundles on proper algebraic varieties. The first (resp. last) minima are the width (resp. Seshadri constant) of the line bundle at very general points. The volume of the line bundle is equivalent to the product of the successive minima. For line bundles on toric varieties, the successive minima are equivalent to the (reciprocal of) usual successive minima of the difference of the moment polytope.
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An injectivity theorem II
We extend the injectivity theorem of Esnault and Viehweg to a class of non-normal log varieties, which contains normal crossings log varieties, and is closed under the operation of taking the $\LCS$ locus.
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On toric face rings II
We introduce the class of weakly log canonical singularities, a natural generalization of semi-log canonical singularities. Toric varieties (associated to toric face rings, possibly non-normal or reducible) which have weakly (semi-) log canonical singularities are classified. In the toric case, we discuss residues to lc centers of codimension one or higher.
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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-canonical pair using its normalization.
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On toric face rings I
We construct an explicit Deligne - Du Bois complex for algebraic varieties which are locally analytically isomorphic to the spectrum of a toric face ring.
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Cyclic covers and toroidal embeddings
We present an improved version of the cyclic covering trick, which works inside the category of toroidal embeddings
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On representations by Egyptian fractions
We give a sharp upper bound for the entries of the representations of a rational number as a sum of Egyptian fractions.
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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 anticanonical members in terms of the global minimal log discrepancy.
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An Injectivity Theorem
We generalize the injectivity theorem of Esnault and Viehweg, and apply it to the structure of log canonical type divisors.
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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.
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The minimal log discrepancy
We survey the known and expected properties of the minimal log discrepancy, the local invariant of a log variety.
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Restrictions of log canonical algebras of general type
We introduce a diophantine property of a log canonical algebra, and use it to describe the restriction of a log canonical algebra of general type to a log canonical center of codimension one.
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