Calabi-Yau Three-folds of Type K (I): Classification

Kenji Hashimoto; Atsushi Kanazawa

doi:10.1093/imrn/rnw197

Calabi-Yau Three-folds of Type K (I): Classification

Kenji Hashimoto, Atsushi Kanazawa

Research output: Contribution to journal › Article › peer-review

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Abstract

Any Calabi-Yau three-fold X with infinite fundamental group admits an étale Galois covering either by an abelian three-fold or by the product of a K3 surface and an elliptic curve.Wecall X of type A in the former case and of type K in the latter case. In this article, we provide the full classification of Calabi-Yau three-folds of type K, based on Oguiso and Sakurai's work [25]. Together with a refinement of their result on Calabi-Yau threefolds of type A, we finally complete the classification of Calabi-Yau three-folds with infinite fundamental group.

Original language	English
Pages (from-to)	6654-6693
Number of pages	40
Journal	International Mathematics Research Notices
Volume	2017
Issue number	21
DOIs	https://doi.org/10.1093/imrn/rnw197
Publication status	Published - 2017 Nov 1
Externally published	Yes

ASJC Scopus subject areas

Mathematics(all)

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10.1093/imrn/rnw197

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title = "Calabi-Yau Three-folds of Type K (I): Classification",

abstract = "Any Calabi-Yau three-fold X with infinite fundamental group admits an {\'e}tale Galois covering either by an abelian three-fold or by the product of a K3 surface and an elliptic curve.Wecall X of type A in the former case and of type K in the latter case. In this article, we provide the full classification of Calabi-Yau three-folds of type K, based on Oguiso and Sakurai's work [25]. Together with a refinement of their result on Calabi-Yau threefolds of type A, we finally complete the classification of Calabi-Yau three-folds with infinite fundamental group.",

author = "Kenji Hashimoto and Atsushi Kanazawa",

note = "Funding Information: It is a pleasure to record our thanks to K. Behrend, J. Bryan, I. Dolgachev, C. Doran, S. Hosono, J. Keum, K. Oguiso, T. Terasoma, and S.-T. Yau for inspiring discussions. Much of this research was done when the first author was supported by Korea Institute for Advanced Study. The second author warmly thanks N. Yui for her hospitality at the Fields Institute, where some of this project was carried out. The second author is supported by the Center of Mathematical Sciences and Applications at Harvard University. Publisher Copyright: {\textcopyright} The Author 2016.",

year = "2017",

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doi = "10.1093/imrn/rnw197",

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T2 - Classification

AU - Hashimoto, Kenji

AU - Kanazawa, Atsushi

N1 - Funding Information: It is a pleasure to record our thanks to K. Behrend, J. Bryan, I. Dolgachev, C. Doran, S. Hosono, J. Keum, K. Oguiso, T. Terasoma, and S.-T. Yau for inspiring discussions. Much of this research was done when the first author was supported by Korea Institute for Advanced Study. The second author warmly thanks N. Yui for her hospitality at the Fields Institute, where some of this project was carried out. The second author is supported by the Center of Mathematical Sciences and Applications at Harvard University. Publisher Copyright: © The Author 2016.

PY - 2017/11/1

Y1 - 2017/11/1

N2 - Any Calabi-Yau three-fold X with infinite fundamental group admits an étale Galois covering either by an abelian three-fold or by the product of a K3 surface and an elliptic curve.Wecall X of type A in the former case and of type K in the latter case. In this article, we provide the full classification of Calabi-Yau three-folds of type K, based on Oguiso and Sakurai's work [25]. Together with a refinement of their result on Calabi-Yau threefolds of type A, we finally complete the classification of Calabi-Yau three-folds with infinite fundamental group.

AB - Any Calabi-Yau three-fold X with infinite fundamental group admits an étale Galois covering either by an abelian three-fold or by the product of a K3 surface and an elliptic curve.Wecall X of type A in the former case and of type K in the latter case. In this article, we provide the full classification of Calabi-Yau three-folds of type K, based on Oguiso and Sakurai's work [25]. Together with a refinement of their result on Calabi-Yau threefolds of type A, we finally complete the classification of Calabi-Yau three-folds with infinite fundamental group.

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IS - 21

ER -

Calabi-Yau Three-folds of Type K (I): Classification

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