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• W3111796728 startingPage "6262" @default.
• W3111796728 abstract "This article is concerned with Chern class and Chern number inequalities on polarized manifolds and nef vector bundles. For a polarized pair $(M,L)$ with $L$ very ample, our first main result is a family of sharp Chern class inequalities. Among them the first one is a variant of a classical result and the equality case of the second one is a characterization of hypersurfaces. The second main result is a Chern number inequality on it, which includes a reverse Miyaoka-Yau type inequality. The third main result is that the Chern numbers of a nef vector bundle over a compact K{a}hler manifold are bounded below by the Euler number. As an application, we classify compact K{a}hler manifolds with nonnegative bisectional curvature whose Chern numbers are all positive. A conjecture related to the Euler number of compact K{a}hler manifolds with nonpositive bisectional curvature is proposed, which can be regarded as a complex analogue to the Hopf conjecture." @default.
• W3111796728 created "2020-12-21" @default.
• W3111796728 creator A5011761321 @default.
• W3111796728 creator A5085587821 @default.
• W3111796728 date "2020-12-08" @default.
• W3111796728 modified "2023-10-03" @default.
• W3111796728 title "Chern Class Inequalities on Polarized Manifolds and Nef Vector Bundles" @default.
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• W3111796728 doi "https://doi.org/10.1093/imrn/rnaa317" @default.
• W3111796728 hasPublicationYear "2020" @default.
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