On the volume of a pseudo-effective class and semi-positive properties of the Harder-Narasimhan filtration on a compact Hermitian manifold | |
Wang, Zhiwei | |
2016 | |
关键词 | volume partial derivative partial derivative-cohomology nef class pseudo-effective class big class closed positive current Gauduchon metric Monge-Ampere equation Harder-Narasimhan filtration stability EFFECTIVE RICCI CLASS NON-KAHLER-MANIFOLDS COMPLEX-MANIFOLDS CHARACTERISTIC ZERO CURRENTS BUNDLES EQUATION THEOREM |
英文摘要 | This paper divides into two parts. Let (X, omega) be a compact Hermitian manifold. Firstly, if the Hermitian metric omega satisfies the assumption that partial derivative(partial derivative) over bar omega(k) = 0 for all k, we generalize the volume of the cohomology class in the Kahler setting to the Hermitian setting, and prove that the volume is always finite and the Grauert-Riemenschneider type criterion holds true, which is a partial answer to a conjecture posed by Boucksom. Secondly, we observe that if the anticanonical bundle K-X(-1) is nef, then for any epsilon > 0, there is a smooth function phi(epsilon) on X such that omega(epsilon) := omega + i partial derivative(partial derivative) over bar phi(epsilon) and Ricci(omega(epsilon)) >= - epsilon omega(epsilon). Furthermore, if omega satisfies the assumption as above, we prove that for a Harder Narasimhan filtration of Tx with respect to omega, the slopes mu(omega) (Fi/Fi-1) are nonnegative for all i; this generalizes a result of Cao which plays an important role in his study of the structures of Kahler manifolds.; SCI(E); ARTICLE; wangzw@amss.ac.cn; 1; 41-58; 117 |
语种 | 英语 |
出处 | SCI |
出版者 | ANNALES POLONICI MATHEMATICI |
内容类型 | 其他 |
源URL | [http://hdl.handle.net/20.500.11897/492549] |
专题 | 数学科学学院 |
推荐引用方式 GB/T 7714 | Wang, Zhiwei. On the volume of a pseudo-effective class and semi-positive properties of the Harder-Narasimhan filtration on a compact Hermitian manifold. 2016-01-01. |
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