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Miyaoka-Yau type inequalities of complete intersection threefolds in products of projective
- 1 Chongqing Depu Foreign Language School
- 2 Chongqing Depu Foreign Language School
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Abstract
Geography of projective varieties is one of the fundamental problems in algebraic geometry. There are many researches toward the characteristics of Chern number of some projective spaces, for example Noether’s inequalities, the theorem of Chang-Lopez, and the Miyaoka-Yau inequality. In this paper, we compute the Chern numbers of any smooth complete intersection threefold in the product of projective spaces via the standard exact sequences of cotangent bundles. Then we obtain linear Chern number inequalities for (c_1 (X)c_2 (X))/(c_1^3 (X)) and (c_3 (X))/(c_1^3 (X)) on such threefolds under conditions of d_ij≥4 and d_ij≥6 respectively. They can be considered as a generalization of the Miyaoka-Yau inequality and an improvement of Yau’s inequality for such threefolds.
Keywords
Chen class, Miyaoka-Yau Inequality, Threefold, Complete Intersection
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Cite this article
Zhang,M.;Zhang,M. (2023). Miyaoka-Yau type inequalities of complete intersection threefolds in products of projective. Theoretical and Natural Science,14,8-17.
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Volume title: Proceedings of the 3rd International Conference on Computing Innovation and Applied Physics
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