Abstract
We investigate the resurgence and asymptotic resurgence numbers of fiber products of projective schemes. Particularly, we show that while the asymptotic resurgence number of the k-fold fiber product of a projective scheme remains unchanged, its resurgence number could strictly increase.
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Acknowledgements
The authors thank Louiza Fouli and Paolo Mantero for pointing out a mistake in the first draft of the paper. The authors also thank Elena Guardo and Alexandra Seceleanu for many stimulating discussions on related topics. Part of this work was done while the third author visited the other authors at Tulane University—the authors thank Tulane University for its hospitality. The second author is partially supported by Louisiana Board of Regents (Grant #LEQSF(2017-19)-ENH-TR-25). The computational commutative algebra package Macaulay 2, [13], has helped us in testing containment between symbolic and ordinary powers which are key to several results in this paper. The authors thank an anonymous referee for many useful comments.
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Bisui, S., Hà, H.T., Jayanthan, A.V. et al. Resurgence numbers of fiber products of projective schemes. Collect. Math. 72, 605–614 (2021). https://doi.org/10.1007/s13348-020-00302-5
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DOI: https://doi.org/10.1007/s13348-020-00302-5