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 dim*H*^{0}(*M*, *L*) = *n* + 1, then *M* is biholomorphic to a complex projective space *P*^{n} of dimension *n*.

Let

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.

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.