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Minuscule Schubert Varieties and Mirror Symmetry
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2017, том 13
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Minuscule Schubert Varieties and Mirror Symmetry
Інший ID:
2010 Mathematics Subject Classification: 14J32; 14J33; 14M15; 14M25
DOI:10.3842/SIGMA.2017.067
DOI:10.3842/SIGMA.2017.067
Посилання:
Minuscule Schubert Varieties and Mirror Symmetry / M. Miura // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 65 назв. — англ.
Підтримка:
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.
Дата:
2017
Переглядів:
411
Завантажень:
229
Анотація:
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.
