Minuscule Schubert Varieties and Mirror Symmetry

We consider smooth complete intersection Calabi-Yau 3-folds in minuscule Schubert varieties, and study their mirror symmetry by degenerating the ambient Schubert varieties to Hibi toric varieties. We list all possible Calabi-Yau 3-folds of this type up to deformation equivalences, and find a new exa...

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Veröffentlicht in:Symmetry, Integrability and Geometry: Methods and Applications
Datum:2017
1. Verfasser: Miura, M.
Format: Artikel
Sprache:English
Veröffentlicht: Інститут математики НАН України 2017
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/148736
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren:Minuscule Schubert Varieties and Mirror Symmetry / M. Miura // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 65 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-148736
record_format dspace
spelling Miura, M.
2019-02-18T18:20:01Z
2019-02-18T18:20:01Z
2017
Minuscule Schubert Varieties and Mirror Symmetry / M. Miura // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 65 назв. — англ.
1815-0659
2010 Mathematics Subject Classification: 14J32; 14J33; 14M15; 14M25
DOI:10.3842/SIGMA.2017.067
https://nasplib.isofts.kiev.ua/handle/123456789/148736
We consider smooth complete intersection Calabi-Yau 3-folds in minuscule Schubert varieties, and study their mirror symmetry by degenerating the ambient Schubert varieties to Hibi toric varieties. We list all possible Calabi-Yau 3-folds of this type up to deformation equivalences, and find a new example of smooth Calabi-Yau 3-folds of Picard number one; a complete intersection in a locally factorial Schubert variety Σ of the Cayley plane OP². We calculate topological invariants and BPS numbers of this Calabi-Yau 3-fold and conjecture that it has a non-trivial Fourier-Mukai partner.
The author would like to express his deep gratitude to his supervisor Professor Shinobu Hosono for valuable suggestions and warm encouragement. He greatly appreciates many helpful discussions with Daisuke Inoue, Atsushi Kanazawa and Fumihiko Sanda at the seminars we had in University of Tokyo. He would also like to thank Yoshinori Gongyo, Takehiko Yasuda, Atsushi Ito and Taro Sano for useful comments to improve the work. The author thanks the anonymous referees for providing a number of valuable comments and in particular for pointing out the oversight of the examples of Picard number two in Proposition 3.1. Part of this paper was written at Mathematisches Institute Universit¨at T¨ubingen during his stay from October 1 to December 25, 2012. He was supported in part by Institutional Program for Young Researcher Overseas Visits by JSPS for this stay. It is a pleasure to thank Professor Victor Batyrev for valuable comments and creating a nice environment for the author.
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Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Minuscule Schubert Varieties and Mirror Symmetry
Article
published earlier
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title Minuscule Schubert Varieties and Mirror Symmetry
spellingShingle Minuscule Schubert Varieties and Mirror Symmetry
Miura, M.
title_short Minuscule Schubert Varieties and Mirror Symmetry
title_full Minuscule Schubert Varieties and Mirror Symmetry
title_fullStr Minuscule Schubert Varieties and Mirror Symmetry
title_full_unstemmed Minuscule Schubert Varieties and Mirror Symmetry
title_sort minuscule schubert varieties and mirror symmetry
author Miura, M.
author_facet Miura, M.
publishDate 2017
language English
container_title Symmetry, Integrability and Geometry: Methods and Applications
publisher Інститут математики НАН України
format Article
description We consider smooth complete intersection Calabi-Yau 3-folds in minuscule Schubert varieties, and study their mirror symmetry by degenerating the ambient Schubert varieties to Hibi toric varieties. We list all possible Calabi-Yau 3-folds of this type up to deformation equivalences, and find a new example of smooth Calabi-Yau 3-folds of Picard number one; a complete intersection in a locally factorial Schubert variety Σ of the Cayley plane OP². We calculate topological invariants and BPS numbers of this Calabi-Yau 3-fold and conjecture that it has a non-trivial Fourier-Mukai partner.
issn 1815-0659
url https://nasplib.isofts.kiev.ua/handle/123456789/148736
citation_txt Minuscule Schubert Varieties and Mirror Symmetry / M. Miura // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 65 назв. — англ.
work_keys_str_mv AT miuram minusculeschubertvarietiesandmirrorsymmetry
first_indexed 2025-12-02T11:37:21Z
last_indexed 2025-12-02T11:37:21Z
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