The author gives a characterization of counterexamples to the Kodaira-Ramanujam vanishing theorem on smooth projective surfaces in positive characteristic.More precisely,it is reproved that if there is a counterexampl...The author gives a characterization of counterexamples to the Kodaira-Ramanujam vanishing theorem on smooth projective surfaces in positive characteristic.More precisely,it is reproved that if there is a counterexample to the Kodaira-Ramanujam vanishing theorem on a smooth projective surface X in positive characteristic,then X is either a quasi-elliptic surface of Kodaira dimension 1 or a surface of general type.Furthermore,it is proved that up to blow-ups,X admits a fibration to a smooth projective curve,such that each fiber is a singular curve.展开更多
A horizontal Hodge Laplacian operator □h is defined for Hermitian holomorphic vector bundles over PTM on Khler Finsler manifold,and the expression of □h is obtained explicitly in terms of horizontal covariant deri...A horizontal Hodge Laplacian operator □h is defined for Hermitian holomorphic vector bundles over PTM on Khler Finsler manifold,and the expression of □h is obtained explicitly in terms of horizontal covariant derivatives of the Chern-Finsler connection.The vanishing theorem is obtained by using the α_Hα_H-method on Kahler Finsler manifolds.展开更多
Let X be a compact complex manifold. Consider a small deformation π ： X → B of X, the dimensions of the cohomology groups of tangent sheaf Hq（xt, Txt ） may vary under this deformation. This article studies such p...Let X be a compact complex manifold. Consider a small deformation π ： X → B of X, the dimensions of the cohomology groups of tangent sheaf Hq（xt, Txt ） may vary under this deformation. This article studies such phenomena by studying the obstructions to deform a class in Hq（X, 5TX） with parameter t and gets a formula for the obstructions.展开更多
In this paper, we generalize the Bochner-Kodaira formulas to the case of Hermitian com- plex (possibly non-holomorphic) vector bundles over compact Hermitian (possibly non-K¨ahler) mani- folds. As applications, w...In this paper, we generalize the Bochner-Kodaira formulas to the case of Hermitian com- plex (possibly non-holomorphic) vector bundles over compact Hermitian (possibly non-K¨ahler) mani- folds. As applications, we get the complex analyticity of harmonic maps between compact Hermitian manifolds.展开更多
This is a continuation of our previous paper [14]. In [14], we introduced the first Aeppli- Chern class on compact complex manifolds, and proved that the （1, 1） curvature form of the Levi-Civita connection represent...This is a continuation of our previous paper [14]. In [14], we introduced the first Aeppli- Chern class on compact complex manifolds, and proved that the （1, 1） curvature form of the Levi-Civita connection represents the first Aeppli-Chern class which is a natural link between Riemannian geometry and complex geometry. In this paper, we study the geometry of compact complex manifolds with Levi- Civita Ricci-flat metrics and classify minimal complex surfaces with Levi-Civita Ricci-flat metrics. More precisely, we show that minimal complex surfaces admitting Levi-Civita Ricci-flat metrics are K/ihler Calabi-Yau surfaces and Hopf surfaces.展开更多
The moduli space of complex structures on S1×S3/H) is studied, where H U(2) is a fi-nite Abelian group whose action is properly discontinuous and free on S3.
基金supported by the National Natural Science Foundation of China (No. 10901037)the Doctoral Program Foundation of the Ministry of Education of China (No. 20090071120004)the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministry
文摘The author gives a characterization of counterexamples to the Kodaira-Ramanujam vanishing theorem on smooth projective surfaces in positive characteristic.More precisely,it is reproved that if there is a counterexample to the Kodaira-Ramanujam vanishing theorem on a smooth projective surface X in positive characteristic,then X is either a quasi-elliptic surface of Kodaira dimension 1 or a surface of general type.Furthermore,it is proved that up to blow-ups,X admits a fibration to a smooth projective curve,such that each fiber is a singular curve.
基金supported by the National Natural Science Foundation of China(No.11712777)the Scientific Research Foundation of Shanghai University of Engineering Science(No.E1-0501-14-0112)
文摘A horizontal Hodge Laplacian operator □h is defined for Hermitian holomorphic vector bundles over PTM on Khler Finsler manifold,and the expression of □h is obtained explicitly in terms of horizontal covariant derivatives of the Chern-Finsler connection.The vanishing theorem is obtained by using the α_Hα_H-method on Kahler Finsler manifolds.
基金partially supported by China-France-Russian mathematics collaboration grant,No.34000-3275100,from Sun Yat-Sen University
文摘Let X be a compact complex manifold. Consider a small deformation π ： X → B of X, the dimensions of the cohomology groups of tangent sheaf Hq（xt, Txt ） may vary under this deformation. This article studies such phenomena by studying the obstructions to deform a class in Hq（X, 5TX） with parameter t and gets a formula for the obstructions.
文摘In this paper, we generalize the Bochner-Kodaira formulas to the case of Hermitian com- plex (possibly non-holomorphic) vector bundles over compact Hermitian (possibly non-K¨ahler) mani- folds. As applications, we get the complex analyticity of harmonic maps between compact Hermitian manifolds.
基金supported in part by NSFC(Grant No.11531012),NSFC(Grant No.11688101)supported in part by China’s Recruitment Program
文摘This is a continuation of our previous paper [14]. In [14], we introduced the first Aeppli- Chern class on compact complex manifolds, and proved that the （1, 1） curvature form of the Levi-Civita connection represents the first Aeppli-Chern class which is a natural link between Riemannian geometry and complex geometry. In this paper, we study the geometry of compact complex manifolds with Levi- Civita Ricci-flat metrics and classify minimal complex surfaces with Levi-Civita Ricci-flat metrics. More precisely, we show that minimal complex surfaces admitting Levi-Civita Ricci-flat metrics are K/ihler Calabi-Yau surfaces and Hopf surfaces.
基金the National Natural Science Foundation of China Natural Science Foundation of Education Committee of Jiangsu Province
文摘The moduli space of complex structures on S1×S3/H) is studied, where H U(2) is a fi-nite Abelian group whose action is properly discontinuous and free on S3.
