no. G8
Géométrie algébrique
Ramified cover of varieties with nef cotangent bundle
Wang, Yiyu1
1 Department of Mathematics, University of Wisconsin - Madison, 480 Lincoln Drive, 213 Van Vleck Hall, Madison, WI 53706, USA
Comptes Rendus. Mathématique, Tome 360 (2022) no. G8, pp. 929-932.

We construct examples to show that having nef cotangent bundle is not preserved under finite ramified covers. Our examples also show that a projective manifold with Stein universal cover may not have nef cotangent bundle, disproving a conjecture of Liu–Maxim–Wang [7].

Reçu le :
Révisé le :
Accepté le :
Publié le :
DOI : 10.5802/crmath.365
Wang, Yiyu 1

1 Department of Mathematics, University of Wisconsin - Madison, 480 Lincoln Drive, 213 Van Vleck Hall, Madison, WI 53706, USA 
@article{CRMATH_2022__360_G8_929_0,
     author = {Wang, Yiyu},
     title = {Ramified cover of varieties with nef cotangent bundle},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {929--932},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {360},
     number = {G8},
     year = {2022},
     doi = {10.5802/crmath.365},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/crmath.365/}
}
TY  - JOUR
AU  - Wang, Yiyu
TI  - Ramified cover of varieties with nef cotangent bundle
JO  - Comptes Rendus. Mathématique
PY  - 2022
SP  - 929
EP  - 932
VL  - 360
IS  - G8
PB  - Académie des sciences, Paris
UR  - http://www.numdam.org/articles/10.5802/crmath.365/
DO  - 10.5802/crmath.365
LA  - en
ID  - CRMATH_2022__360_G8_929_0
ER  - 
%0 Journal Article
%A Wang, Yiyu
%T Ramified cover of varieties with nef cotangent bundle
%J Comptes Rendus. Mathématique
%D 2022
%P 929-932
%V 360
%N G8
%I Académie des sciences, Paris
%U http://www.numdam.org/articles/10.5802/crmath.365/
%R 10.5802/crmath.365
%G en
%F CRMATH_2022__360_G8_929_0
Wang, Yiyu. Ramified cover of varieties with nef cotangent bundle. Comptes Rendus. Mathématique, Tome 360 (2022) no. G8, pp. 929-932. doi : 10.5802/crmath.365. http://www.numdam.org/articles/10.5802/crmath.365/

[1] Arapura, Donu; Wang, Botong Perverse sheaves on varieties with large fundamental groups (2021) | arXiv

[2] Grauert, Hans; Remmert, Reinhold Applications of Theorems A and B, Springer (2004), pp. 125-185

[3] Kollár, János Shafarevich maps and plurigenera of algebraic varieties, Invent. Math., Volume 113 (1993) no. 1, pp. 177-215 | DOI | MR | Zbl

[4] Kratz, Henrik Compact complex manifolds with numerically effective cotangent bundles, Doc. Math., Volume 2 (1997), pp. 183-193 | MR | Zbl

[5] Lazarsfeld, Robert Positivity in Algebraic Geometry I: Classical Setting: Line Bundles and Linear Series, Springer, 2004

[6] Lazarsfeld, Robert Positivity in Algebraic Geometry II: Positivity for Vector Bundles, and Multiplier Ideals, Springer, 2004

[7] Liu, Yongqiang; Maxim, Laurenţiu; Wang, Botong Aspherical manifolds, Mellin transformation and a question of Bobadilla–Kollár, J. Reine Angew. Math., Volume 781 (2021), pp. 1-18 | Zbl

[8] Shiffman, Bernard; Zaidenberg, Mikhail Hyperbolic hypersurfaces in ℙ n of Fermat–Waring type, Proc. Am. Math. Soc., Volume 130 (2002) no. 7, pp. 2031-2035 | DOI | MR | Zbl

[9] Sommese, Andrew John On the density of ratios of Chern numbers of algebraic surfaces, Math. Ann., Volume 268 (1984) no. 2, pp. 207-221 | DOI | MR | Zbl

[10] Stein, Karl Überlagerungen holomorph-vollständiger komplexer Räume, Arch. Math., Volume 7 (1956) no. 5, pp. 354-361 | DOI | MR | Zbl

Cité par Sources :