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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dc.contributor.author	Miura, M.
dc.date.accessioned	2019-02-18T18:20:01Z
dc.date.available	2019-02-18T18:20:01Z
dc.date.issued	2017
dc.identifier.citation	Minuscule Schubert Varieties and Mirror Symmetry / M. Miura // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 65 назв. — англ.	uk_UA
dc.identifier.issn	1815-0659
dc.identifier.other	2010 Mathematics Subject Classification: 14J32; 14J33; 14M15; 14M25
dc.identifier.other	DOI:10.3842/SIGMA.2017.067
dc.identifier.uri	http://dspace.nbuv.gov.ua/handle/123456789/148736
dc.description.abstract	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.	uk_UA
dc.description.sponsorship	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.	uk_UA
dc.language.iso	en	uk_UA
dc.publisher	Інститут математики НАН України	uk_UA
dc.relation.ispartof	Symmetry, Integrability and Geometry: Methods and Applications
dc.title	Minuscule Schubert Varieties and Mirror Symmetry	uk_UA
dc.type	Article	uk_UA
dc.status	published earlier	uk_UA