About the Hyperbolicity of Complete Intersections

 Access to full text

 Full (PDF)

 Full (DjVu)

1. BROTBEK, D., Hyperbolicity Related Problems for Complete Intersection Varieties, ArXiv e-prints, January 2011. MR3187623DOI10.1112/S0010437X13007458
2. CANTAT, S., Deux exemples concernant une conjecture de Serge Lang, C. R. Acad. Sci. Paris Sér. I Math., 330, no. 7 (2000), 581-586. MR1760443DOI10.1016/S0764-4442(00)00226-3
3. DEBARRE, O., Varieties with ample cotangent bundle, Compos. Math., 141, no. 6 (2005), 1445-1459. Zbl1086.14038MR2188444DOI10.1112/S0010437X05001399
4. DEMAILLY, J.-P., Algebraic criteria for Kobayashi hyperbolic projective varieties and jet differentials, Algebraic geometry-Santa Cruz 1995, 285-360, Proc. Sympos. Pure Math., 62, Part 2, Amer. Math. Soc., Providence, RI, 1997. MR1492539DOI10.1090/pspum/062.2/1492539
5. DEMAILLY, J.-P., Holomorphic Morse inequalities and the Green-Griffiths-Lang conjecture, Pure Appl. Math. Q., 7, no. 4 (2011), Special Issue: In memory of Eckart Viehweg, 1165-1207. Zbl1316.32014MR2918158DOI10.4310/PAMQ.2011.v7.n4.a6
6. DEMAILLY, J.-P. - EL GOUL, J., Hyperbolicity of generic surfaces of high degree in projective 3-space, Amer. J. Math., 122, no. 3 (2000), 515-546. Zbl0966.32014MR1759887
7. DESCHAMPS, M., Courbes de genre géométrique borné sur une surface de type général [d'après F. A. Bogomolov], Séminaire Bourbaki, 30e année (1977/78), Exp. No. 519, pp. 233-247, Lecture Notes in Math., 710, Springer, Berlin, 1979. MR554224
8. DIVERIO, S., Existence of global invariant jet differentials on projective hypersurfaces of high degree, Math. Ann., 344, no. 2 (2009), 293-315. Zbl1166.32013MR2495771DOI10.1007/s00208-008-0306-4
9. DIVERIO, S. - FERRETTI, A., On a conjecture of Oguiso about rational curves on Calabi-Yau threefolds, to appear on Comment. Math. Helv. Zbl1304.14049MR3177911DOI10.4171/CMH/315
10. DIVERIO, S. - MERKER, J. - ROUSSEAU, E., Effective algebraic degeneracy, Invent. Math., 180, no. 1 (2010), 161-223. Zbl1192.32014MR2593279DOI10.1007/s00222-010-0232-4
11. DIVERIO, S. - TRAPANI, S., A remark on the codimension of the Green-Griffiths locus of generic projective hypersurfaces of high degree, J. Reine Angew. Math., 649 (2010), 55-61. Zbl1211.32015MR2746466DOI10.1515/CRELLE.2010.088
12. EIN, L., Subvarieties of generic complete intersections, Invent. Math., 94, no. 1 (1988), 163-169. Zbl0701.14002MR958594DOI10.1007/BF01394349
13. GREEN, M. - GRIFFITHS, P., Two applications of algebraic geometry to entire holomorphic mappings, The Chern Symposium 1979 (Proc. Internat. Sympos., Berkeley, Calif., 1979), 41-74, Springer, New York-Berlin, 1980. MR609557
14. HEATH-BROWN, D. R. - WILSON, P. M. H., Calabi-Yau threefolds with $\rho >13$, Math. Ann., 294, no. 1 (1992), 49-57. MR1180449DOI10.1007/BF01934312
15. KOBAYASHI, S., Hyperbolic complex spaces, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 318. Springer-Verlag, Berlin, 1998. MR1635983DOI10.1007/978-3-662-03582-5
16. LANG, S., Higher dimensional diophantine problems, Bull. Amer. Math. Soc., 80 (1974), 779-787. Zbl0298.14014MR360464DOI10.1090/S0002-9904-1974-13516-0
17. LANG, S., Hyperbolic and Diophantine analysis, Bull. Amer. Math. Soc. (N.S.), 14, no. 2 (1986), 159-205. MR828820DOI10.1090/S0273-0979-1986-15426-1
18. MCQUILLAN, M., Diophantine approximations and foliations, Inst. Hautes Études Sci. Publ. Math. No. 87 (1998), 121-174. Zbl1006.32020MR1659270
19. MCQUILLAN, M., Holomorphic curves on hyperplane sections of 3-folds, Geom. Funct. Anal., 9, no. 2 (1999), 370-392. Zbl0951.14014MR1692470DOI10.1007/s000390050091
20. MERKER, J., Low pole order frames on vertical jets of the universal hypersurface, Ann. Inst. Fourier (Grenoble), 59, no. 3 (2009), 1077-1104. Zbl1172.32005MR2543663
21. MORI, S. - MUKAI, S., The uniruledness of the moduli space of curves of genus 11; In Algebraic geometry (Tokyo/Kyoto, 1982), volume 1016 of Lecture Notes in Math., pages 334-353. Springer, Berlin, 1983. MR726433DOI10.1007/BFb0099970
22. OGUISO, K., On algebraic fiber space structures on a Calabi-Yau 3-fold, Internat. J. Math., 4, no. 3 (1993), 439-465. Zbl0793.14030MR1228584DOI10.1142/S0129167X93000248
23. PĂUN, M., Vector fields on the total space of hypersurfaces in the projective space and hyperbolicity, Math. Ann., 340, no. 4 (2008), 875-892. Zbl1137.32010MR2372741DOI10.1007/s00208-007-0172-5
24. PETERNELL, T., Calabi-Yau manifolds and a conjecture of Kobayashi, Math. Z., 207, no. 2 (1991), 305-318. MR1109668DOI10.1007/BF02571390
25. ROUSSEAU, E., Weak analytic hyperbolicity of generic hypersurfaces of high degree in ${\mathbb{P}}^4$, Ann. Fac. Sci. Toulouse Math. (6), 16, no. 2 (2007), 369-383. Zbl1132.32010MR2331545
26. SIU, Y.-T., Hyperbolicity in complex geometry, The legacy of Niels Henrik Abel (Springer, Berlin, 2004), 543-566. Zbl1076.32011MR2077584
27. SIU, Y.-T., Hyperbolicity of Generic High-Degree Hypersurfaces in Complex Projective Spaces, ArXiv e-prints, October 2012. MR3425387DOI10.1007/s00222-015-0584-x
28. SIU, Y.-T. - YEUNG, S.-K., Hyperbolicity of the complement of a generic smooth curve of high degree in the complex projective plane, Invent. Math., 124, no. 1-3 (1996), 573- 618. MR1369429DOI10.1007/s002220050064
29. VOISIN, C., On a conjecture of Clemens on rational curves on hypersurfaces, J. Differential Geom., 44, no. 1 (1996), 200-213. Zbl0883.14022MR1420353
30. VOISIN, C., A correction: ``On a conjecture of Clemens on rational curves on hypersurfaces [J. Differential Geom. 44 (1996), no. 1, 200-213; MR1420353 (97j:14047)]'', J. Differential Geom., 49, no. 3 (1998), 601-611. Zbl0883.14022MR1669712