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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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2017 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2017
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/148736 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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| _version_ | 1862661240611930112 |
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| author | Miura, M. |
| author_facet | Miura, M. |
| citation_txt | Minuscule Schubert Varieties and Mirror Symmetry / M. Miura // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 65 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-12-02T11:37:21Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-148736 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-02T11:37:21Z |
| publishDate | 2017 |
| publisher | Інститут математики НАН України |
| 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Minuscule Schubert Varieties and Mirror Symmetry Article published earlier |
| spellingShingle | Minuscule Schubert Varieties and Mirror Symmetry Miura, M. |
| title | 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_short | Minuscule Schubert Varieties and Mirror Symmetry |
| title_sort | minuscule schubert varieties and mirror symmetry |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148736 |
| work_keys_str_mv | AT miuram minusculeschubertvarietiesandmirrorsymmetry |