A proof of the birationality of certain BHK-mirrors

Patrick Clarke

Complex Manifolds (2014)

  • Volume: 1, Issue: 1, page 45-51, electronic only
  • ISSN: 2300-7443

Abstract

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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].

How to cite

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Patrick Clarke. "A proof of the birationality of certain BHK-mirrors." Complex Manifolds 1.1 (2014): 45-51, electronic only. <http://eudml.org/doc/276959>.

@article{PatrickClarke2014,
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].},
author = {Patrick Clarke},
journal = {Complex Manifolds},
keywords = {BHK-mirrors, birationality},
language = {eng},
number = {1},
pages = {45-51, electronic only},
title = {A proof of the birationality of certain BHK-mirrors},
url = {http://eudml.org/doc/276959},
volume = {1},
year = {2014},
}

TY - JOUR
AU - Patrick Clarke
TI - A proof of the birationality of certain BHK-mirrors
JO - Complex Manifolds
PY - 2014
VL - 1
IS - 1
SP - 45
EP - 51, electronic only
AB - 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].
LA - eng
KW - BHK-mirrors, birationality
UR - http://eudml.org/doc/276959
ER -

References

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  1. [1] Victor V. Batyrev. Dual polyhedra and mirror symmetry for Calabi-Yau hypersurfaces in toric varieties. J. Algebraic Geom., 3(3):493–535, 1994. Zbl0829.14023
  2. [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. Zbl0842.32023
  3. [3] Lev Borisov. Towards the Mirror Symmetry for Calabi-Yau Complete intersections in Gorenstein Toric Fano Varieties. 
  4. [4] Patrick Clarke. Duality for toric Landau-Ginzburg models. 
  5. [5] Patrick Clarke. Berglund-Hübsch-Krawitz duality as Duality for toric Landau-Ginzburg models. University of Michigan RTG Workshop on Mirror Symmetry, 2012. 
  6. [6] Alexander B. Givental. Equivariant Gromov-Witten invariants. Internat. Math. Res. Notices, (13):613–663, 1996. Zbl0881.55006
  7. [7] B. R. Greene and M. R. Plesser. Duality in Calabi-Yau moduli space. Nuclear Phys. B, 338(1):15–37, 1990. 
  8. [8] Kentaro Hori and Cumrun Vafa. Mirror Symmetry. 
  9. [9] Tyler Kelly. Berglund-Hüsch-krawitz Mirrors via Shioda Maps. Advances in Theoretical and Mathematical Physics. to appear. [WoS] Zbl1316.14076
  10. [10] Marc Krawitz. FJRW rings and Landau-Ginzburg mirror symmetry. ProQuest LLC, Ann Arbor, MI, 2010. Thesis (Ph.D.)– University of Michigan. Zbl1250.81087
  11. [11] Mark Shoemaker. Birationality of Berglund-Hübsch-Krawitz Mirrors. [WoS] Zbl06346281

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