Abstract
The authors compute the (rational) Betti number of real toric varieties associated to Weyl chambers of type B, and furthermore show that their integral cohomology is p-torsion free for all odd primes p.
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Acknowledgments
The authors thank to Prof. Soojin Cho for helpful discussions, and Prof. Jang Soo Kim for suggesting nice proof of Lemma 3.1. They are also thankful to the anonymous referee for the thorough reading and kind comments.
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This work was supported by the Basic Science Research Program through the National Research Foundation of Korea (Nos.NRF-2016R1D1A1A09917654, NRF-2015R1C1A1A01053495).
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Choi, S., Park, B. & Park, H. The Betti numbers of real toric varieties associated to Weyl chambers of type B. Chin. Ann. Math. Ser. B 38, 1213–1222 (2017). https://doi.org/10.1007/s11401-017-1032-6
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DOI: https://doi.org/10.1007/s11401-017-1032-6
Keywords
- Real toric variety
- Real toric manifold
- Betti number
- Torsion-free cohomology
- Root system
- Weyl chambers
- Type B
- Generalized Euler number
- Springer number
- Shellability