TY - JOUR
T1 - On the image of mrc fibrations of projective manifolds with semi-positive holomorphic sectional curvature
AU - Matsumura, Shin Ichi
N1 - Funding Information:
The author wishes to express his gratitude to Professor Junyan Cao for suggesting Conjecture 1.1 and for many stimulating conversations. He wishes to express his gratitude to Professor Xiaokui Yang for useful discussions on [27] and to Professor Yoshinori Gongyo for kindly answering questions of algebraic geometry. He also would like to thank the members of Institut de Math?matiques de Jussieu-Paris Rive gauche for their hospitality during my stay. He is supported by the Grant-in-Aid for Young Scientists (A) ?17H04821, Fostering Joint International Research (A) ?19KK0342, Advancing Strategic International Networks to Accelerate the Circulation of Talented Researchers, from JSPS.
Publisher Copyright:
© 2020, Homology, Homotopy and Applications. All rights reserved.
PY - 2020
Y1 - 2020
N2 - In this paper, we pose several conjectures on structures and images of maximal rationally connected fibrations of smooth projective varieties admitting semi-positive holomorphic sectional curvature. Toward these conjectures, we prove that the canonical bundle of images of such fibrations is not big. Our proof gives a generalization of Yang’s solution using RC positivity for Yau’s conjecture. As an application, we show that any compact Kähler surface with semi-positive holomorphic sectional curvature is rationally connected, or a complex torus, or a ruled surface over an elliptic curve.
AB - In this paper, we pose several conjectures on structures and images of maximal rationally connected fibrations of smooth projective varieties admitting semi-positive holomorphic sectional curvature. Toward these conjectures, we prove that the canonical bundle of images of such fibrations is not big. Our proof gives a generalization of Yang’s solution using RC positivity for Yau’s conjecture. As an application, we show that any compact Kähler surface with semi-positive holomorphic sectional curvature is rationally connected, or a complex torus, or a ruled surface over an elliptic curve.
KW - Abelian varieties
KW - Holomorphic sectional curvatures
KW - Maximal rationally connected fibrations
KW - Minimal models
KW - RC positivity
KW - Ruled surfaces
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U2 - 10.4310/PAMQ.2020.v16.n5.a3
DO - 10.4310/PAMQ.2020.v16.n5.a3
M3 - Article
AN - SCOPUS:85102470336
VL - 16
SP - 1419
EP - 1439
JO - Pure and Applied Mathematics Quarterly
JF - Pure and Applied Mathematics Quarterly
SN - 1558-8599
IS - 5
ER -