Log canonical models of foliated surfaces

Chen, Yenan

doi:10.48550/arxiv.2103.12669

Cited by 2 publications

(2 citation statements)

References 8 publications

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“…Analogous results for a more restricted class of foliated pairs have recently appeared also in [Che21]. We remark that these results, together with the work in [Che21], provide an important step toward showing the existence of a moduli space for surface foliations.…”

Section: Introductionsupporting

confidence: 74%

Effective generation for foliated surfaces: results and applications

Spicer¹,

Svaldi²

2021

Preprint

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We prove some results on the birational structure and invariants of a foliated surface (X, F) in terms of the adjoint divisor KF + ǫKX , 0 < ǫ ≪ 1. Several applications of these ideas are considered as well. Contents 1. Introduction 1 2. Preliminaries 4 3. Adjoint MMP 14 4. A bound on the pseudo-effective threshold in the big case 17 5. Applications 23 6. Boundedness of ample models 24 References 30

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Section: Introductionsupporting

confidence: 74%

Effective generation for foliated surfaces: results and applications

Spicer¹,

Svaldi²

2021

Preprint

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“…For example, the abundance conjecture fails in general, even for surfaces [McQ08,Theorem 3 IV.5.11], and effective birationality also fails in general [SS22, Paragraph after Problem 1]. As a result, the boundedness of foliations of general type can only be proved for surfaces under certain additional assumptions [Che21a,Che21c,HL21a,SS22].…”

Section: Introductionmentioning

confidence: 99%

On global ACC for foliated threefolds

Liu¹,

Luo²,

Meng³

2023

Preprint

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In this paper, we prove the rational coefficient case of the global ACC for foliated threefolds. Specifically, we consider any lc foliated log Calabi-Yau triple (X, F, B) of dimension 3 whose coefficients belong to a set Γ of rational numbers satisfying the descending chain condition, and prove that the coefficients of B belong to a finite set depending only on Γ.To prove our main result, we introduce the concept of generalized foliated quadruples, which is a mixture of foliated triples and Birkar-Zhang's generalized pairs. With this concept, we establish a canonical bundle formula for foliations in any dimension.As for applications, we extend Shokurov's global index conjecture in the classical MMP to foliated triples and prove this conjecture for threefolds with nonzero boundaries and for surfaces. Additionally, we introduce the theory of rational polytopes for functional divisors on foliations and prove some miscellaneous results.

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Log canonical models of foliated surfaces

Cited by 2 publications

References 8 publications

Effective generation for foliated surfaces: results and applications

Effective generation for foliated surfaces: results and applications

On global ACC for foliated threefolds

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