Comptes Rendus
Géométrie algébrique
Bigness of the tangent bundles of projective bundles over curves
Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1115-1122.

In this short article, we determine the bigness of the tangent bundle T X of the projective bundle X= C (E) associated to a vector bundle E on a smooth projective curve C.

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DOI : 10.5802/crmath.476

Jeong-Seop Kim 1

1 School of Mathematics, Korea Institute for Advanced Study, 85 Hoegiro Dongdaemun-gu, Seoul 02455, Republic of Korea
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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     title = {Bigness of the tangent bundles of projective bundles over curves},
     journal = {Comptes Rendus. Math\'ematique},
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     year = {2023},
     doi = {10.5802/crmath.476},
     language = {en},
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Jeong-Seop Kim. Bigness of the tangent bundles of projective bundles over curves. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1115-1122. doi : 10.5802/crmath.476. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.476/

[1] Michael F. Atiyah Vector bundles over an elliptic curve, Proc. Lond. Math. Soc., Volume 7 (1957), pp. 414-452 | DOI | MR | Zbl

[2] Thomas Bauer; Sándor J. Kovács; Alex Küronya; Ernesto C. Mistretta; Tomasz Szemberg; Stefano Urbinati On positivity and base loci of vector bundles, Eur. J. Math., Volume 1 (2015) no. 2, pp. 229-249 | DOI | MR | Zbl

[3] Frédéric Campana; Thomas Peternell Projective manifolds whose tangent bundles are numerically effective, Math. Ann., Volume 289 (1991) no. 1, pp. 169-187 | DOI | MR | Zbl

[4] Frédéric Campana; Thomas Peternell 4-folds with numerically effective tangent bundles and second Betti numbers greater than one, Manuscr. Math., Volume 79 (1993) no. 3-4, pp. 225-238 | DOI | MR | Zbl

[5] Andreas Höring; Jie Liu Fano manifolds with big tangent bundle: a characterisation of V 5 , Collect. Math., Volume 74 (2023) no. 3, pp. 639-686 | DOI | MR | Zbl

[6] Andreas Höring; Jie Liu; Feng Shao Examples of Fano manifolds with non-pseudoeffective tangent bundle, J. Lond. Math. Soc., Volume 106 (2022) no. 1, pp. 27-59 | DOI | MR | Zbl

[7] Daniel Huybrechts; Manfred Lehn The geometry of moduli spaces of sheaves, Cambridge University Press, 2010 | DOI

[8] Jun-Muk Hwang Rigidity of rational homogeneous spaces, Proceedings of the international congress of mathematicians (ICM). Volume II: Invited lectures, European Mathematical Society, 2006, pp. 613-626 | Zbl

[9] Jun-Muk Hwang; Sundararaman Ramanan Hecke curves and Hitchin discriminant, Ann. Sci. Éc. Norm. Supér., Volume 37 (2004) no. 5, pp. 801-817 | DOI | Numdam | MR | Zbl

[10] Akihiro Kanemitsu Fano 5-folds with nef tangent bundles, Math. Res. Lett., Volume 24 (2017) no. 5, pp. 1453-1475 | DOI | MR | Zbl

[11] Hosung Kim; Jeong-Seop Kim; Yongnam Lee Bigness of the tangent bundle of a Fano threefold with Picard number two (2022) | arXiv

[12] János Kollár; Shigefumi Mori Birational geometry of algebraic varieties, Cambridge Tracts in Mathematics, 134, Cambridge University Press, 1998 (with the collaboration of C. H. Clemens and A. Corti, Translated from the 1998 Japanese original) | DOI

[13] Robert Lazarsfeld Positivity in algebraic geometry. I. Classical setting: line bundles and linear series, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge, 48, Springer, 2004

[14] Robert Lazarsfeld Positivity in algebraic geometry. II. Positivity for vector bundles, and multiplier ideals, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge, 49, Springer, 2004 | DOI

[15] Yoichi Miyaoka The Chern classes and Kodaira dimension of a minimal variety, Algebraic geometry, Sendai, 1985 (Advanced Studies in Pure Mathematics), Volume 10, North-Holland, 1987, pp. 449-476 | DOI | MR | Zbl

[16] Ngaiming Mok On Fano manifolds with nef tangent bundles admitting 1-dimensional varieties of minimal rational tangents, Trans. Am. Math. Soc., Volume 354 (2002) no. 7, pp. 2639-2658 | MR | Zbl

[17] Shigefumi Mori Projective manifolds with ample tangent bundles, Ann. Math., Volume 110 (1979) no. 3, pp. 593-606 | DOI | MR | Zbl

[18] Shigeru Mukai; Fumio Sakai Maximal subbundles of vector bundles on a curve, Manuscr. Math., Volume 52 (1985) no. 1-3, pp. 251-256 | DOI | MR | Zbl

[19] Roberto Muñoz; Gianluca Occhetta; Luis E. Solá Conde; Kiwamu Watanabe; Jarosław A. Wiśniewski A survey on the Campana-Peternell conjecture, Rend. Ist. Mat. Univ. Trieste, Volume 47 (2015), pp. 127-185 | MR | Zbl

[20] Mudumbai S. Narasimhan; Sundararaman Ramanan Moduli of vector bundles on a compact Riemann surface, Ann. Math., Volume 89 (1969), pp. 14-51 | DOI | MR | Zbl

[21] Gianluca Occhetta; Luis E. Solá Conde; Kiwamu Watanabe Uniform families of minimal rational curves on Fano manifolds, Rev. Mat. Complut., Volume 29 (2016) no. 2, pp. 423-437 | DOI | MR | Zbl

[22] Jeff Rosoff Effective divisor classes on a ruled surface, Pac. J. Math., Volume 202 (2002) no. 1, pp. 119-124 | DOI | MR | Zbl

[23] Michał Szurek; Jarosław A. Wiśniewski Fano bundles of rank 2 on surfaces, Compos. Math., Volume 76 (1990) no. 1-2, pp. 295-305 | Numdam | MR | Zbl

[24] Kiwamu Watanabe Fano 5-folds with nef tangent bundles and Picard numbers greater than one, Math. Z., Volume 276 (2014) no. 1-2, pp. 39-49 | DOI | MR | Zbl

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