Abstract
The authors study torsion in the integral cohomology of a certain family of 2n-dimensional orbifolds X with actions of the n-dimensional compact torus. Compact simplicial toric varieties are in our family. For a prime number p, the authors find a necessary condition for the integral cohomology of X to have no p-torsion. Then it is proved that the necessary condition is sufficient in some cases. The authors also give an example of X which shows that the necessary condition is not sufficient in general.
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Acknowledgments
We thank Tony Bahri, Soumen Sarkar and Jongbaek Song for their interest and useful comments on the paper. We also thank Matthias Franz for his comments and for his development of the Maple package torhom which was very useful in our research. Finally we thank the anonymous referee for helpful comments to improve the presentation of the paper.
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This work was supported by JSPS Grant-in-Aid for Scientific Research (No. 25400095).
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Kuwata, H., Masuda, M. & Zeng, H. Torsion in the cohomology of torus orbifolds. Chin. Ann. Math. Ser. B 38, 1247–1268 (2017). https://doi.org/10.1007/s11401-017-1034-4
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DOI: https://doi.org/10.1007/s11401-017-1034-4