Holomorphic one-forms on varieties of general type
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 38 (2005) no. 4, pp. 599-607.
@article{ASENS_2005_4_38_4_599_0,
     author = {Hacon, Christopher D. and Kov\'acs, S\'andor J.},
     title = {Holomorphic one-forms on varieties of general type},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {599--607},
     publisher = {Elsevier},
     volume = {Ser. 4, 38},
     number = {4},
     year = {2005},
     doi = {10.1016/j.ansens.2004.12.002},
     mrnumber = {2172952},
     zbl = {1083.14015},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/j.ansens.2004.12.002/}
}
TY  - JOUR
AU  - Hacon, Christopher D.
AU  - Kovács, Sándor J.
TI  - Holomorphic one-forms on varieties of general type
JO  - Annales scientifiques de l'École Normale Supérieure
PY  - 2005
SP  - 599
EP  - 607
VL  - 38
IS  - 4
PB  - Elsevier
UR  - http://archive.numdam.org/articles/10.1016/j.ansens.2004.12.002/
DO  - 10.1016/j.ansens.2004.12.002
LA  - en
ID  - ASENS_2005_4_38_4_599_0
ER  - 
%0 Journal Article
%A Hacon, Christopher D.
%A Kovács, Sándor J.
%T Holomorphic one-forms on varieties of general type
%J Annales scientifiques de l'École Normale Supérieure
%D 2005
%P 599-607
%V 38
%N 4
%I Elsevier
%U http://archive.numdam.org/articles/10.1016/j.ansens.2004.12.002/
%R 10.1016/j.ansens.2004.12.002
%G en
%F ASENS_2005_4_38_4_599_0
Hacon, Christopher D.; Kovács, Sándor J. Holomorphic one-forms on varieties of general type. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 38 (2005) no. 4, pp. 599-607. doi : 10.1016/j.ansens.2004.12.002. http://archive.numdam.org/articles/10.1016/j.ansens.2004.12.002/

[1] Akyıldız E., Carrell J.B., Zeros of holomorphic vector fields and the Gysin homomorphism, in: Singularities, Part 1, Arcata, CA, 1981, Proc. Sympos. Pure Math., vol. 40, American Mathematical Society, Providence RI, 1983, pp. 47-54, MR713044 (85c:32020). | Zbl

[2] Akyıldız E., Carrell J.B., Lieberman D.I., Zeros of holomorphic vector fields on singular spaces and intersection rings of Schubert varieties, Compositio Math. 57 (2) (1986) 237-248, MR827353 (87j:32086). | Numdam | Zbl

[3] Akyıldız E., Carrell J.B., Lieberman D.I., Sommese A.J., On the graded rings associated to holomorphic vector fields with exactly one zero, in: Singularities, Part 1, Arcata, CA, 1981, Proc. Sympos. Pure Math., vol. 40, American Mathematical Society, Providence, RI, 1983, pp. 55-56, MR713045 (84i:14029). | Zbl

[4] Baum P., Bott R., On the zeros of meromorphic vector-fields, in: Essays on Topology and Related Topics, Mémoires dédiés à Georges de Rham, Springer, New York, 1970, pp. 29-47, MR0261635 (41 #6248). | MR | Zbl

[5] Baum P., Bott R., Singularities of holomorphic foliations, J. Differential Geom. 7 (1972) 279-342, MR0377923 (51 #14092). | MR | Zbl

[6] Bott R., Vector fields and characteristic numbers, Michigan Math. J. 14 (1967) 231-244, MR0211416 (35 #2297). | MR | Zbl

[7] Carrell J.B., Holomorphic one forms and characteristic numbers, Topology 13 (1974) 225-228, MR0348147 (50 #645). | MR | Zbl

[8] Carrell J., Howard A., Kosniowski C., Holomorphic vector fields on complex surfaces, Math. Ann. 204 (1973) 73-81, MR0372262 (51 #8478). | MR | Zbl

[9] Carrell J.B., Lieberman D.I., Holomorphic vector fields and Kaehler manifolds, Invent. Math. 21 (1973) 303-309, MR0326010 (48 #4356). | MR | Zbl

[10] Carrell J.B., Lieberman D.I., Vector fields and Chern numbers, Math. Ann. 225 (3) (1977) 263-273, MR0435456 (55 #8416). | MR | Zbl

[11] Du Bois P., Complexe de de Rham filtré d'une variété singulière, Bull. Soc. Math. France 109 (1) (1981) 41-81, MR613848 (82j:14006). | Numdam | MR | Zbl

[12] Elkik R., Singularités rationnelles et déformations, Invent. Math. 47 (2) (1978) 139-147, MR501926 (80c:14004). | MR | Zbl

[13] Elkik R., Rationalité des singularités canoniques, Invent. Math. 64 (1) (1981) 1-6, MR621766 (83a:14003). | MR | Zbl

[14] Fulton W., Intersection Theory, Ergebnisse der Mathematik und ihrer Grenzgebiete (3), vol. 2, Springer-Verlag, Berlin, 1984, MR732620 (85k:14004). | MR | Zbl

[15] Griffiths P., Harris J., Algebraic geometry and local differential geometry, Ann. Sci. École Norm. Sup. (4) 12 (3) (1979) 355-452, MR559347 (81k:53004). | Numdam | MR | Zbl

[16] Green M., Lazarsfeld R., Deformation theory, generic vanishing theorems, and some conjectures of Enriques, Catanese and Beauville, Invent. Math. 90 (2) (1987) 389-407, MR910207 (89b:32025). | MR | Zbl

[17] Guillén F., Navarro Aznar V., Pascual Gainza P., Puerta F., Hyperrésolutions cubiques et descente cohomologique, Lecture Notes in Mathematics, vol. 1335, Springer, Berlin, 1988, Papers from the Seminar on Hodge-Deligne Theory held in Barcelona, 1982, MR972983 (90a:14024). | MR | Zbl

[18] Hartshorne R., Algebraic Geometry, Graduate Texts in Mathematics, vol. 52, Springer, New York, 1977, MR0463157 (57 #3116). | MR | Zbl

[19] Kawamata Y., Minimal models and the Kodaira dimension of algebraic fiber spaces, J. reine angew. Math. 363 (1985) 1-46, MR814013 (87a:14013). | MR | Zbl

[20] Kollár J., Mori S., Birational Geometry of Algebraic Varieties, Cambridge Tracts in Mathematics, vol. 134, Cambridge University Press, Cambridge, 1998, With the collaboration of C.H. Clemens and A. Corti, Translated from the 1998 Japanese original, MR1658959 (2000b:14018). | MR | Zbl

[21] Kovács S.J., Families over a base with a birationally nef tangent bundle, Math. Ann. 308 (2) (1997) 347-359, MR1464907 (98h:14039). | MR | Zbl

[22] Kovács S.J., A characterization of rational singularities, Duke Math. J. 102 (2) (2000) 187-191, MR1749436 (2002b:14005). | MR | Zbl

[23] Kovács, S.J., Spectral sequences associated to morphisms of locally free sheaves, in preparation.

[24] Luo T., Zhang Q., Holomorphic forms on threefolds, math.AG/0304022. | MR

[25] Mori S., Classification of higher-dimensional varieties, in: Algebraic Geometry, Bowdoin, 1985, Brunswick, Maine, 1985, Proc. Sympos. Pure Math., vol. 46, American Mathematical Society, Providence, RI, 1987, pp. 269-331, MR927961 (89a:14040). | MR | Zbl

[26] Reid M., Minimal models of canonical 3-folds, in: Algebraic Varieties and Analytic Varieties, Tokyo, 1981, Adv. Stud. Pure Math., vol. 1, North-Holland, Amsterdam, 1983, pp. 131-180, MR715649 (86a:14010). | MR | Zbl

[27] Ueno K., Classification Theory of Algebraic Varieties and Compact Complex Spaces, Lecture Notes in Mathematics, vol. 439, Springer, Berlin, 1975, Notes written in collaboration with P. Cherenack, MR0506253 (58 #22062). | MR | Zbl

[28] Viehweg E., Zuo K., On the isotriviality of families of projective manifolds over curves, J. Algebraic Geom. 10 (4) (2001) 781-799, MR1838979 (2002g:14012). | MR | Zbl

[29] Zhang Q., Global holomorphic one-forms on projective manifolds with ample canonical bundles, J. Algebraic Geom. 6 (4) (1997) 777-787, MR1487236 (99k:14071). | MR | Zbl

Cité par Sources :