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Complex Manifolds

Ed. by Fino, Anna Maria

Covered by Web of Science - Emerging Sources Citation Index and Zentralblatt Math (zbMATH)


CiteScore 2018: 0.64

SCImago Journal Rank (SJR) 2018: 0.643
Source Normalized Impact per Paper (SNIP) 2018: 0.812

Mathematical Citation Quotient (MCQ) 2018: 0.61

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2300-7443
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A proof of the birationality of certain BHK-mirrors

Patrick Clarke
Published Online: 2014-08-06 | DOI: https://doi.org/10.2478/coma-2014-0003

Abstract

We generalize and give an elementary proof of Kelly’s refinement [9] of Shoemaker’s result [11] on the birationality of certain BHK-mirrors. Our approach uses a construction that is equivalent to the Krawitz generalization [10] of the duality in Berglund-Hübsch [2].

References

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  • [2] Per Berglund and Tristan Hübsch. A generalized construction of mirror manifolds. In Essays on mirror manifolds, pages 388–407. Int. Press, Hong Kong, 1992. Google Scholar

  • [3] Lev Borisov. Towards the Mirror Symmetry for Calabi-Yau Complete intersections in Gorenstein Toric Fano Varieties. Google Scholar

  • [4] Patrick Clarke. Duality for toric Landau-Ginzburg models. Google Scholar

  • [5] Patrick Clarke. Berglund-Hübsch-Krawitz duality as Duality for toric Landau-Ginzburg models. University of Michigan RTG Workshop on Mirror Symmetry, 2012. Google Scholar

  • [6] Alexander B. Givental. Equivariant Gromov-Witten invariants. Internat. Math. Res. Notices, (13):613–663, 1996. Google Scholar

  • [7] B. R. Greene and M. R. Plesser. Duality in Calabi-Yau moduli space. Nuclear Phys. B, 338(1):15–37, 1990. Google Scholar

  • [8] Kentaro Hori and Cumrun Vafa. Mirror Symmetry. Google Scholar

  • [9] Tyler Kelly. Berglund-Hüsch-krawitz Mirrors via Shioda Maps. Advances in Theoretical and Mathematical Physics. to appear. Web of ScienceGoogle Scholar

  • [10] Marc Krawitz. FJRW rings and Landau-Ginzburg mirror symmetry. ProQuest LLC, Ann Arbor, MI, 2010. Thesis (Ph.D.)– University of Michigan. Google Scholar

  • [11] Mark Shoemaker. Birationality of Berglund-Hübsch-Krawitz Mirrors. Web of ScienceGoogle Scholar

About the article

Received: 2014-03-28

Accepted: 2014-06-03

Published Online: 2014-08-06


Citation Information: Complex Manifolds, Volume 1, Issue 1, ISSN (Online) 2300-7443, DOI: https://doi.org/10.2478/coma-2014-0003.

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© 2014 Patrick Clarke. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]
David Favero and Tyler L. Kelly
Advances in Mathematics, 2019, Volume 352, Page 943
[2]
Lev A. Borisov and Zhan Li
Advances in Mathematics, 2018, Volume 328, Page 300
[3]
Patrick Clarke
Communications in Mathematical Physics, 2017, Volume 353, Number 3, Page 1241
[4]
Patrick Clarke
Advances in Mathematics, 2016, Volume 301, Page 902

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