Theoretical and Natural Science
- The Open Access Proceedings Series for Conferences
Theoretical and Natural Science
Vol. 14, 30 November 2023
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Miyaoka-Yau type inequalities of complete intersection threefolds in products of projective
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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
References
1. Christian, & Liedtke. (2008). Algebraic surfaces of general type with small c21 in positive characteristic. Nagoya Mathematical Journal.
2. S.-T., Y. (1977). Calabi’s conjecture and some new results in algebraic geometry. Proceedings of the National Academy of Sciences.
3. Bruce, & Hunt. (1989). Complex manifold geography in dimension {2} and {3}. Journal of Differential Geometry.
4. Mei-Chu, ChangAngelo, Felice, & Lopez. (2001). A linear bound on the euler number of threefolds of calabi–yau and of general type. Manuscripta Mathematica.
5. Sheng, M. , Xu, J. , & Zhang, M. . (2014). On the chern number inequalities satisfied by all smooth complete intersection threefolds with ample canonical class. International Journal of Mathematics, 25(4), 1450029-.
6. Du, R., & Sun, H. (2017). Inequalities of chern classes on nonsingular projective n-folds of fano or general type with ample canonical bundle.
Data Availability
The datasets used and/or analyzed during the current study will be available from the authors upon reasonable request.
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- Volume Title
- Proceedings of the 3rd International Conference on Computing Innovation and Applied Physics
- ISBN (Print)
- 978-1-83558-191-9
- ISBN (Online)
- 978-1-83558-192-6
- Published Date
- 30 November 2023
- Series
- Theoretical and Natural Science
- ISSN (Print)
- 2753-8818
- ISSN (Online)
- 2753-8826
- DOI
- 10.54254/2753-8818/14/20240867
- Copyright
- 30 November 2023
- Open Access
- This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited