Download this article
Download this article For screen
For printing
Recent Issues

Volume 30
Issue 5, 1611–2042
Issue 4, 1203–1610
Issue 3, 835–1201
Issue 2, 389–833
Issue 1, 1–388

Volume 29, 9 issues

Volume 28, 9 issues

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
 
Author index
To appear
 
Other MSP journals
Positivity and the Kodaira embedding theorem

Lei Ni and Fangyang Zheng

Geometry & Topology 26 (2022) 2491–2505
DOI: 10.2140/gt.2022.26.2491
Bibliography
1 G Heier, B Wong, On projective Kähler manifolds of partially positive curvature and rational connectedness, Doc. Math. 25 (2020) 219 MR4106891
2 N Hitchin, On the curvature of rational surfaces, from: "Differential geometry, II" (editors S S Chern, R Osserman), Proc. Symp. Pure Math. 27, Amer. Math. Soc. (1975) 65 MR0400127
3 R A Horn, C R Johnson, Matrix analysis, Cambridge Univ. Press (2013) MR2978290
4 S Kobayashi, Differential geometry of complex vector bundles, 15, Princeton Univ. Press (1987) MR909698
5 J Kollár, Y Miyaoka, S Mori, Rationally connected varieties, J. Algebraic Geom. 1 (1992) 429 MR1158625
6 G Liu, Three-circle theorem and dimension estimate for holomorphic functions on Kähler manifolds, Duke Math. J. 165 (2016) 2899 MR3557275
7 J Morrow, K Kodaira, Complex manifolds, Holt, Rinehart and Winston (1971) MR0302937
8 L Ni, Vanishing theorems on complete Kähler manifolds and their applications, J. Differential Geom. 50 (1998) 89 MR1678481
9 L Ni, The fundamental group, rational connectedness and the positivity of Kähler manifolds, J. Reine Angew. Math. 774 (2021) 267 MR4250473
10 L Ni, Liouville theorems and a Schwarz lemma for holomorphic mappings between Kähler manifolds, Comm. Pure Appl. Math. 74 (2021) 1100 MR4230067
11 L Ni, F Zheng, Comparison and vanishing theorems for Kähler manifolds, Calc. Var. Partial Differential Equations 57 (2018) MR3858834
12 L Ni, F Zheng, On orthogonal Ricci curvature, from: "Advances in complex geometry" (editors Y A Rubinstein, B Shiffman), Contemp. Math. 735, Amer. Math. Soc. (2019) 203 MR3996490
13 Y Tsukamoto, On Kählerian manifolds with positive holomorphic sectional curvature, Proc. Japan Acad. 33 (1957) 333 MR90845
14 C Voisin, On the homotopy types of compact Kähler and complex projective manifolds, Invent. Math. 157 (2004) 329 MR2076925
15 D Wu, S T Yau, Negative holomorphic curvature and positive canonical bundle, Invent. Math. 204 (2016) 595 MR3489705
16 X Yang, RC-positivity, rational connectedness and Yau’s conjecture, Camb. J. Math. 6 (2018) 183 MR3811235
17 S T Yau, Problem section, from: "Seminar on differential geometry" (editor S T Yau), Ann. of Math. Stud. 102, Princeton Univ. Press (1982) 669 MR645762