2021
DOI: 10.1017/s1474748020000754
|View full text |Cite
|
Sign up to set email alerts
|

On Projective Manifolds With Pseudo-Effective Tangent Bundle

Abstract: In this paper, we develop the theory of singular Hermitian metrics on vector bundles. As an application, we give a structure theorem of a projective manifold X with pseudo-effective tangent bundle; X admits a smooth fibration $X \to Y$ to a flat projective manifold Y such that its general fibre is rationally connected. Moreover, by applying this structure theorem, we classify all the minimal surfaces with pseudo-effective tangent bundle and study general nonminimal surfaces, which p… Show more

Help me understand this report
View preprint versions

Search citation statements

Order By: Relevance

Paper Sections

Select...
2
2

Citation Types

1
16
0

Year Published

2021
2021
2024
2024

Publication Types

Select...
6
1

Relationship

1
6

Authors

Journals

citations
Cited by 23 publications
(17 citation statements)
references
References 32 publications
1
16
0
Order By: Relevance
“…Paris [39, Proposition 3.2.3 and Proposition 3.2.4] and Hosono, Iwai and Matsumura [19, Proposition 4.5 and Proposition 4.8] obtained similar results for the tangent bundle of rational surfaces, but their definition of pseudoeffectiveness is (at least a priori) strictly stronger than ours. Note that Mallory proved, with completely different techniques, that TX$T_X$ is not big if d4$d \leqslant 4$ [34, Corollary 5.7].…”
Section: Introductionsupporting
confidence: 67%
See 3 more Smart Citations
“…Paris [39, Proposition 3.2.3 and Proposition 3.2.4] and Hosono, Iwai and Matsumura [19, Proposition 4.5 and Proposition 4.8] obtained similar results for the tangent bundle of rational surfaces, but their definition of pseudoeffectiveness is (at least a priori) strictly stronger than ours. Note that Mallory proved, with completely different techniques, that TX$T_X$ is not big if d4$d \leqslant 4$ [34, Corollary 5.7].…”
Section: Introductionsupporting
confidence: 67%
“…An elementary computation using (19) shows that this intersection number is −8, a contradiction. Hence, by Corollary 2.6 there exists a unique prime divisor ⊂ ℙ(𝑇 𝑋 ) generating the extremal ray ℝ + 𝜁.…”
Section: Del Pezzo Threefolds Of Degree Twomentioning
confidence: 93%
See 2 more Smart Citations
“…On the other hand, the pioneering studies ( [Mor79,SY80]) have demonstrated that the structures of varieties with "semipositive" curvature have a certain rigidity and are closely related to the geometry of rational curves. Based on this philosophy, several structure theorems and uniformization theorems have been established for Albanese maps or maximal rationally connected (MRC) fibrations of varieties, under various positivity assumptions of the curvature; including non-negative holomorphic bisectional curvatures ([HSW81, MZ86,Mok88]), nonnegative holomorphic sectional curvatures ([Yan16, HW20, Mat18]), nef tangent bundles ([CP91, DPS94]), pseudo-effective tangent bundles ( [HIM19]), and nef anti-canonical divisors ([Cao19, CH19, DLB20]). In particular, the study of projective manifolds with nef anti-canonical divisor covers a large range of varieties with "non-negative" curvature; moreover, the study of such varieties is more natural from the viewpoint of birational geometry than that of varieties with positive tangent bundles.…”
mentioning
confidence: 99%