A Characterization of Complex Projective Spaces by Sections of Line Bundles
ABSTRACT
Let M be a n-dimensional compact irreducible complex space with a line bundle L. It is shown that if M is completely intersected with respect to L and dimH0(M, L) = n + 1, then M is biholomorphic to a complex projective space Pn of dimension n.
Let M be a n-dimensional compact irreducible complex space with a line bundle L. It is shown that if M is completely intersected with respect to L and dimH0(M, L) = n + 1, then M is biholomorphic to a complex projective space Pn of dimension n.
Cite this paper
Liang, S. , Gao, Y. and Zhao, Y. (2015) A Characterization of Complex Projective Spaces by Sections of Line Bundles. Advances in Pure Mathematics, 5, 450-453. doi: 10.4236/apm.2015.58044.
Liang, S. , Gao, Y. and Zhao, Y. (2015) A Characterization of Complex Projective Spaces by Sections of Line Bundles. Advances in Pure Mathematics, 5, 450-453. doi: 10.4236/apm.2015.58044.
References
[1] Kobayashi, S. and Ochiai, T. (1973) Characterizations of Complex Projective Spaces and Hyperquadrics. Journal of Mathematics of Kyoto University, 13, 31-47. [2] Siu, Y.T. and Yau, S.T. (1980) Complex Kahler Manifolds of Positive Bisectional Curvature. Inventiones Mathematicae, 59, 189-204. http://dx.doi.org/10.1007/BF01390043 [3] Mori, S. (1979) Projective Manifolds with Ample Tangent Bundles. Annals of Mathematics, 110, 593-606. http://dx.doi.org/10.2307/1971241 [4] Peternell, T. (1990) A Characterization of Pn by Vector Bundles. Mathematische Zeitschrift, 205, 487-490. http://dx.doi.org/10.1007/BF02571257 [5] Fujita, T. (1989) Remarks on Quasi-Polarized Varieties. Nagoya Mathematical Journal, 115, 105-123. [6] Ye, Y. and Zhang, Q. (1990) On Ample Vector Bundles Whose Adjunction Bundles Are Not Numerically Effective. Duke Mathematical Journal, 60, 671-687.
http://dx.doi.org/10.1215/S0012-7094-90-06027-2 [7] Cho, K., Miyaoka, Y. and Shepherd-Barron, N.I. (2002) Characterizations of Projective Space and Applications to Complex Symplectic Manifolds. Advanced Studies in Pure Mathematics, 35, 1-89. [8] Hirzebruch, F. (1966) Topological Methods in Algebraic Geometry. Springer Verlag, Berlin. [9] Gunning, R. and Rossi, H. (1965) Analytic Functions of Several Complex Varieties. Prentice Hall, Inc., Upper Saddle River.
[1] Kobayashi, S. and Ochiai, T. (1973) Characterizations of Complex Projective Spaces and Hyperquadrics. Journal of Mathematics of Kyoto University, 13, 31-47. [2] Siu, Y.T. and Yau, S.T. (1980) Complex Kahler Manifolds of Positive Bisectional Curvature. Inventiones Mathematicae, 59, 189-204. http://dx.doi.org/10.1007/BF01390043 [3] Mori, S. (1979) Projective Manifolds with Ample Tangent Bundles. Annals of Mathematics, 110, 593-606. http://dx.doi.org/10.2307/1971241 [4] Peternell, T. (1990) A Characterization of Pn by Vector Bundles. Mathematische Zeitschrift, 205, 487-490. http://dx.doi.org/10.1007/BF02571257 [5] Fujita, T. (1989) Remarks on Quasi-Polarized Varieties. Nagoya Mathematical Journal, 115, 105-123. [6] Ye, Y. and Zhang, Q. (1990) On Ample Vector Bundles Whose Adjunction Bundles Are Not Numerically Effective. Duke Mathematical Journal, 60, 671-687.
http://dx.doi.org/10.1215/S0012-7094-90-06027-2 [7] Cho, K., Miyaoka, Y. and Shepherd-Barron, N.I. (2002) Characterizations of Projective Space and Applications to Complex Symplectic Manifolds. Advanced Studies in Pure Mathematics, 35, 1-89. [8] Hirzebruch, F. (1966) Topological Methods in Algebraic Geometry. Springer Verlag, Berlin. [9] Gunning, R. and Rossi, H. (1965) Analytic Functions of Several Complex Varieties. Prentice Hall, Inc., Upper Saddle River.