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The Hartogs Extension Phenomenon in Toric Varieties

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Abstract

We study the Hartogs extension phenomenon in non-compact toric varieties and its relation to the first cohomology group with compact support. We show that a toric variety admits this phenomenon if at least one connected component of the fan complement is concave, proving by this an earlier conjecture M. Marciniak.

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Acknowledgements

This work is supported by the Krasnoyarsk Mathematics Center and financed by the Ministry of Science and Higher Education of the Russian Federation in the framework of the establishment and development of regional Centers for Mathematics Research and Education (Agreement No. 075-02-2020-1534/1). The authors are grateful to the reviewer for a careful reading of the manuscript and comments that helped to improve the readability and quality of the paper.

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  1. Siberian Federal University, Krasnoyarsk, Russia

    Sergey Feklistov

  2. Krasnoyarsk Mathematics Center, Siberian Federal University, Krasnoyarsk, Russia

    Alexey Shchuplev

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  1. Sergey Feklistov
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  2. Alexey Shchuplev
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Correspondence to Alexey Shchuplev.

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Feklistov, S., Shchuplev, A. The Hartogs Extension Phenomenon in Toric Varieties. J Geom Anal 31, 12034–12052 (2021). https://doi.org/10.1007/s12220-021-00710-4

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