EULER CHARACTERISTIC OF TANGO BUNDLES

Authors

  • Nguyen Hong Cong Asia Pacific College, Viet Nam
  • Dang Tuan Hiep Dalat University, Viet Nam
  • Nguyen Thi Mai Van Quy Nhon University, Viet Nam

DOI:

https://doi.org/10.37569/DalatUniversity.12.2.956(2022)

Keywords:

Euler characteristic, Tango bundle.

Abstract

We are interested in a vector bundle constructed by Tango (1976). The Tango bundle is an indecomposable vector bundle of rank \(n-1\) on the complex projective space \(\mathbb{P}^n\). In particular, we show that the Euler characteristic of the Tango bundle on \(\mathbb{P}^n\) is equal to \(2n-1\).

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References

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Dang, T. H. (2014). Intersection theory with applications to the computation of Gromov–Witten invariants. [Doctoral dissertation, Technical University of Kaiserslautern, Germany].

Hirzebruch, F. (1978). Topological methods in algebraic geometry. Springer.

Jaczewski, K., Szurek, M., & Wisniewski, J. A. (1986). Geometry of the Tango bundle. In H. Kurke & M. Roczen (Eds.), Proceedings of the Conference on Algebraic Geometry (Berlin, Germany, 1985) (pp. 177-185). B.G. Teubner.

Okonek, C., Schneider, M., & Spindler, H. (1980). Vector bundles on complex projective spaces, with an appendix by S. I. Gelfand. Birkhäuser (Corrected reprint 2011 by Springer Basel AG). https://doi.org/10.1007/978-3-0348-0151-5

Roman, S. (1984). The umbral calculus. Academic Press.

Tango, H. (1976). An example of indecomposable vector bundle of rank n-1 on P^n. Journal of Mathematics of Kyoto University, 16(1), 137-141. https://doi.org/10.1215/kjm/1250522965

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Published

28-01-2022

Volume and Issues

Section

Natural Sciences and Technology

How to Cite

Nguyen, H. C., Dang, T. H., & Nguyen, T. M. V. (2022). EULER CHARACTERISTIC OF TANGO BUNDLES. Dalat University Journal of Science, 12(2), 113-122. https://doi.org/10.37569/DalatUniversity.12.2.956(2022)