Studies on singular Hermitian metrics and their applications in algebraic geometry

[LSY13] K. Liu, X. Sun, X. Yang. Positivity and vanishing theorems for ample vector bundles. J.

Algebraic Geom. 22 (2013), no. 2, 303–331.

[Mat16] S. Matsumura. A vanishing theorem of Koll´

ar-Ohsawa type. Math. Ann. 366 (2016), no. 3-4,

1451–1465.

[Mat18a] S. Matsumura. On morphisms of compact K¨

ahler manifolds with semi-positive holomorphic

sectional curvature, Preprint, arXiv:1809.08859v1.

[Mat18b] S. Matsumura. On the image of MRC fibrations of projective manifolds with semi-positive

holomorphic sectional curvature, Preprint, arXiv:1801.09081v1.

[MR82] V.B. Mehta, A. Ramanathan. Semistable sheaves on projective varieties and their restriction

to curves. Math. Ann. 258 (1981/82), no. 3, 213–224.

[Miy87] Y. Miyaoka. The Chern classes and Kodaira dimension of a minimal variety. Algebraic geometry, Sendai, 1985, 449–476, Adv. Stud. Pure Math., 10, North-Holland, Amsterdam, 1987.

[Mok88] N. Mok. The uniformization theorem for compact K¨

ahler manifolds of nonnegative holomorphic bisectional curvature, J. Differential Geom. 27 (1988), no. 2, 179–214.

[Mor79] S. Mori. Projective manifolds with ample tangent bundles, Ann. of Math. (2) 110 (1979), no.

3, 593–606.

[MOS+15] R. Mu˜oz, G. Occhetta, L. D. Sol´a Conde, K. Watanabe, J. A.Wi´sniewski. A survey on the

Campana-Peternell conjecture, Rend. Istit. Mat. Univ. Trieste 47 (2015), 127–185.

[Nak04] N. Nakayama. Zariski-decomposition and abundance, MSJ Memoirs, 14. Mathematical Society

of Japan, Tokyo, 2004. xiv+277 pp. ISBN: 4-931469-31-0.

[NZ18] L. NI, F. Zheng. Positivity and Kodaira embedding theorem arXiv:1804.09696

[Ohs84] T. Ohsawa. V anishing theorems on complete K¨ahler manifolds. Publ. Res. Inst. Math. Sci.

20 (1984), no. 1, 21–38.

[PS14] M. Popa, C. Schnell. On direct images of pluricanonical bundles. Algebra Number Theory. 8

(2014), no. 9, 2273-2295.

[Pau16] M. P˘aun. Singular hermitian metrics and positivity of direct images of pluricanonical bundles.

arXiv:1606.00174v1

[PT18] M. P˘aun, S. Takayama. Positivity of twisted relative pluricanonical divisors and their direct

images, J. Algebraic Geom. 27 (2018), 211–272.

[Rau15] H. Raufi. Singular hermitian metrics on holomorphic vector bundles. Ark. Mat. 53 (2015),

no. 2, 359–382.

[Suw69] T. Suwa. On ruled surfaces of genus 1, J. Math. Soc. Japan 21 (1969) 291–311.

[SY80] Y.-T. Siu, S.-T. Yau. Compact K¨

ahler manifolds of positive bisectional curvature, Invent. Math.

59 (1980), no. 2, 189–204.

[Vie83a] E. Viehweg. Weak positivity and the additivity of the Kodaira dimension for certain fibre

spaces. Adv. Stud. Pure Math., 1, (1983) , North-Holland, Amsterdam. 329–353.

[Vie83b] E. Viehweg. Weak positivity and the additivity of the Kodaira dimension. II. The local Torelli

map. Progr. Math., 39, (1983), Birkh¨auser Boston, Boston, MA. 567–589.

[Wang19] J. Wang. On the Iitaka Conjecture Cn,m for K¨

ahler Fibre Spaces Preprint, arXiv:1907.06705

[Yan17] X. Yang. Scalar curvature on compact complex manifolds arXiv:1705.02672

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