2019
DOI: 10.1016/j.matpur.2019.04.007
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On projective varieties with strictly nef tangent bundles

Abstract: In this paper, we study smooth complex projective varieties X such that some exterior power r TX of the tangent bundle is strictly nef. We prove that such varieties are rationally connected. We also classify the following two cases. If TX is strictly nef, then X isomorphic to the projective space P n . If 2 TX is strictly nef and if X has dimension at least 3, then X is either isomorphic to P n or a quadric Q n .

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Cited by 16 publications
(17 citation statements)
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“…Propositions 6.1, 6.5 and 6.6), and hence finally give a positive answer to Question 1.2 for smooth threefolds. This also extends [LOY19, Theorem 1.2] to the pair case (X, ∆) when dim X = 3.…”
Section: Introductionsupporting
confidence: 69%
“…Propositions 6.1, 6.5 and 6.6), and hence finally give a positive answer to Question 1.2 for smooth threefolds. This also extends [LOY19, Theorem 1.2] to the pair case (X, ∆) when dim X = 3.…”
Section: Introductionsupporting
confidence: 69%
“…The purpose of this paper is to provide a structure theorem of smooth projective varieties with nef 2 T X , which gives generalizations of some results in [6,12,33,46,52,53]. Our first result is an analogue of Theorem 1.1: Theorem 1.5.…”
Section: Introductionmentioning
confidence: 91%
“…Related to these results, following the solution of the Hartshorne conjecture [39], K. Cho and E. Sato [12] proved that a smooth projective variety X with ample 2 T X is isomorphic to a projective space or a quadric. Recently, D. Li, W. Ou and X. Yang [33,Theorem 1.5] generalized this result for varieties X with strictly nef 2 T X .…”
Section: Introductionmentioning
confidence: 95%
“…Recently, Li, the second author and the fourth author proved in [LOY19] that smooth projective varieties with strictly nef anti-canonical divisors are rationally connected ([LOY19, Theorems 1.2 and 1.3]). By the well-known result of Campana and Kollár-Mori-Miyaoka ([Cam92,KMM92]), this provides important evidences for an affirmative answer to the Campana and Peternell conjecture, i.e., the smooth case of Conjecture 1.1 in all dimensions.…”
mentioning
confidence: 99%