We prove that Hori-Vafa mirror models for smooth Fano complete intersections in weighted projective spaces admit an interpretation as Laurent polynomials.
@article{bwmeta1.element.doi-10_2478_s11533-011-0070-7,
author = {Victor Przyjalkowski},
title = {Hori-Vafa mirror models for complete intersections in weighted projective spaces and weak Landau-Ginzburg models},
journal = {Open Mathematics},
volume = {9},
year = {2011},
pages = {972-977},
zbl = {1236.14038},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0070-7}
}
Victor Przyjalkowski. Hori-Vafa mirror models for complete intersections in weighted projective spaces and weak Landau-Ginzburg models. Open Mathematics, Tome 9 (2011) pp. 972-977. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0070-7/
[1] Dimca A., Singularities and coverings of weighted complete intersections, J. Reine Angew. Math., 1986, 366, 184–193 http://dx.doi.org/10.1515/crll.1986.366.184 | Zbl 0576.14047
[2] Dolgachev I., Weighted projective varieties, In: Group Actions and Vector Fields, Vancouver, 1981, Lecture Notes in Math., 956, Springer, Berlin, 1982, 34–71 http://dx.doi.org/10.1007/BFb0101508
[3] Douai A., Construction de variétés de Frobenius via les polynômes de Laurent: une autre approche, In: Singularités, Inst. Élie Cartan, 18, Université de Nancy, Nancy, 2005, 105–123
[4] Douai A., Mann E., The small quantum cohomology of a weighted projective space, a mirror D-module and their classical limits, preprint available at http://arxiv.org/abs/0909.4063 | Zbl 1273.14112
[5] Givental A., Equivariant Gromov-Witten invariants, Int. Math. Res. Not., 1996, 613–663 | Zbl 0881.55006
[6] Hori K., Vafa C., Mirror symmetry, preprint available at http://arxiv.org/abs/hep-th/0002222 | Zbl 1044.14018
[7] Ilten N.O., Przyjalkowski V., Toric degenerations of Fano threefolds giving weak Landau-Ginzburg models, preprint available at http://arxiv.org/abs/1102.4664 | Zbl 1270.14020
[8] Przyjalkowski V.V., Quantum cohomology of smooth complete intersections in weighted projective spaces and in singular toric varieties, Mat. Sb., 2007, 198(9), 107–122 | Zbl 1207.14059
[9] Przyjalkowski V., On Landau-Ginzburg models for Fano varieties, Commun. Number Theory Phys., 2008, 1(4), 713–728 | Zbl 1194.14065
[10] Przyjalkowski V., Weak Landau-Ginzburg models for smooth Fano threefolds, preprint available at http://arxiv.org/abs/0902.4668 | Zbl 1281.14033