On the B-Semiampleness Conjecture

Floris, Enrica; Lazić, Vladimir

doi:10.46298/epiga.2019.volume3.5063

Cited by 8 publications

(10 citation statements)

References 15 publications

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“…In this section, we prove Theorems 1.4 and 1.5. The proof of Theorem 1.4 is similar to [Hu20, Subsection 3.4] (see also [FL19,Proposition 4.4]) whose ideas were originated in [FG14]. For the reader's convenience, we give a full proof here.…”

Section: Canonical Bundle Formula: the General Casementioning

confidence: 96%

On generalized lc pairs with $\mathrm{\textbf b}$-log abundant nef part

Jiao¹,

Liu²,

Xie³

2022

Preprint

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We study the behavior of generalized lc pairs with b-log abundant nef part, a meticulously designed structure on algebraic varieties. We show that this structure is preserved under the canonical bundle formula and sub-adjunction formulas, and is also compatible with the non-vanishing conjecture and the abundance conjecture in the classical minimal model program. * A canonical bundle formula for a projective surjective morphism f is given as the composition of a Fujino-Gongyo type canonical bundle formula [FG12] and a Kodaira type canonical bundle formula [Kod63] via the Stein factorization of f . We refer the reader to Subsection 2.4 formal definitions.

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Section: Canonical Bundle Formula: the General Casementioning

confidence: 96%

On generalized lc pairs with $\mathrm{\textbf b}$-log abundant nef part

Jiao¹,

Liu²,

Xie³

2022

Preprint

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“…In this paper we consider a connected divisor T = ∪T and assume the B-Semiampleness Conjecture in lower dimension. In [FL19] we proved that the divisor M Y | T is semiample for every T . In this work we show that we can glue the global sections of mM Y | T to obtain global sections of mM Y | T .…”

Section: Introductionmentioning

confidence: 95%

“…Remark 2.10. As in [FL19], we adopt here the notation B f , M f for the discriminant and moduli part of f instead of the usual one B Y , M Y . We will occasionally write B Y , M Y when the fibration is clear from the contest.…”

Section: Canonical Bundle Formulamentioning

confidence: 99%

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On the restriction of the moduli part to a reduced divisor

Floris¹

2021

Preprint

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Let f : (X, ∆) → Y be a fibration such that KX + ∆ is torsion along the fibres of f . Assume that the fibres have dimension at most 3 or that Y has dimension 2. Assuming the B-Semiampleness conjecture in lower dimension, we prove that the restriction of the moduli part to a reduced, not necessarily irreducible, divisor is semiample.Date: November 8, 2021. This project started during the collaboration with V. Lazić for [FL19]. I am very grateful to Vlad for all the fruitful preliminary discussions around Theorem 10.1 without which this paper would not have been possible. I am very grateful to G. Bini, Y. Brunebarbe, P. Cascini, G. Pacienza, A. Petracci A. Sarti and R. Svaldi for many useful conversations. I was supported by the ANR project "FIBALGA" ANR-18-CE40-0003 and the PEPS JCJC BFC 210024.

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“…Finally, we should point out that [Flo14,FL19] develop inductive approaches towards the effective adjunction conjecture from other perspectives. It is an interesting question to adopt their methods in the current context.…”

Section: Introductionmentioning

confidence: 99%