Geodesic
On the Calabi--Yau Compactifications of Toric Landau--Ginzburg Models for Fano Complete Intersections
Matematičeskie zametki, Tome 103 (2018) no. 1, pp. 111-119.

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It is well known that Givental's toric Landau–Ginzburg models for Fano complete intersections admit Calabi–Yau compactifications. We give an alternative proof of this fact. As a consequence of this proof, we obtain a description of the fibers over infinity of the compactified toric Landau–Ginzburg models.
Mots-clés : Calabi–Yau compactification
Keywords: toric Landau–Ginzburg model, complete intersection. 
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V. V. Przyjalkowski. On the Calabi--Yau Compactifications of Toric Landau--Ginzburg Models for Fano Complete Intersections. Matematičeskie zametki, Tome 103 (2018) no. 1, pp. 111-119. http://geodesic.mathdoc.fr/item/MZM_2018_103_1_a9/

[1] A. Givental, “A mirror theorem for toric complete intersections”, Topological Field Theory, Primitive Forms and Related Topics, Progr. Math., 160, Birkhäuser Boston, Boston, MA, 1998, 141–175 | MR | Zbl

[2] K. Hori, C. Vafa, Mirror Symmetry, 2000, arXiv: hep-th/0002222

[3] V. V. Przhiyalkovskii, “Slabye modeli Landau–Ginzburga gladkikh trekhmernykh mnogoobrazii Fano”, Izv. RAN. Ser. matem., 77:4 (2013), 135–160 | DOI | MR | Zbl

[4] N. O. Ilten, J. Lewis, V. Przyjalkowski, “Toric degenerations of Fano threefolds giving weak Landau–Ginzburg models”, J. Algebra, 374 (2013), 104–121 | DOI | MR | Zbl

[5] V. Przyjalkowski, C. Shramov, “On Hodge numbers of complete intersections and Landau–Ginzburg models”, Int. Math. Res. Not. IMRN, 2015:21 (2015), 11302–11332 | DOI | MR | Zbl

[6] D. Auroux, L. Katzarkov, D. Orlov, “Mirror symmetry for Del Pezzo surfaces: vanishing cycles and coherent sheaves”, Inv. Math., 166:3 (2006), 537–582 | DOI | MR | Zbl

[7] L. Katzarkov, M. Kontsevich, T. Pantev, “Bogomolov–Tian–Todorov theorems for Landau–Ginzburg models”, J. Differential Geom., 105:1 (2017), 55–117 | DOI | MR | Zbl

[8] V. Lunts, V. Przyjalkowski, Landau–Ginzburg Hodge Numbers for Mirrors of Del Pezzo Surfaces, 2016, arXiv: 1607.08880

[9] V. V. Przhiyalkovskii, “Kompaktifikatsii Kalabi–Yau toricheskikh modelei Landau–Ginzburga gladkikh trekhmernykh mnogoobrazii Fano”, Matem. sb., 208:7 (2017), 84–108 | DOI | MR

[10] T. Coates, A. Corti, S. Galkin, A. Kasprzyk, “Quantum periods for 3-dimensional Fano manifolds”, Geom. Topol., 20:1 (2016), 103–256 | DOI | MR | Zbl

[11] Yu. I. Manin, Frobeniusovy mnogoobraziya, kvantovye kogomologii i prostranstva modulei, Faktorial, M., 2002

[12] V. Przyjalkowski, “On Landau–Ginzburg models for Fano varieties”, Commun. Number Theory Phys., 1:4 (2008), 713–728 | DOI | MR | Zbl

[13] S. O. Gorchinskii, D. V. Osipov, “Nepreryvnye gomomorfizmy mezhdu algebrami iterirovannykh ryadov Lorana nad koltsom”, Sovremennye problemy matematiki, mekhaniki i matematicheskoi fiziki. II, Tr. MIAN, 294, MAIK, M., 2016, 54–75 | DOI | MR

[14] S. O. Gorchinskii, D. V. Osipov, “Mnogomernyi simvol Kontu-Karrera i nepreryvnye avtomorfizmy”, Funkts. analiz i ego pril., 50:4 (2016), 26–42 | DOI | MR | Zbl

[15] S. O. Gorchinskii, D. V. Osipov, “Mnogomernyi simvol Kontu-Karrera: lokalnaya teoriya”, Matem. sb., 206:9 (2015), 21–98 | DOI | MR | Zbl

[16] T. Coates, A. Corti, S. Galkin, V. Golyshev, A. Kasprzyk, Fano Varieties and Extremal Laurent Polynomials, A Collaborative Research Blog http://coates.ma.ic.ac.uk/fanosearch/

[17] N. Ilten, A. Kasprzyk, L. Katzarkov, V. Przyjalkowski, D. Sakovics, Projecting Fanos in the Mirror, Preprint

[18] C. Doran, A. Harder, L. Katzarkov, J. Lewis, V. Przyjalkowski, Modularity of Fano Threefolds, Preprint

[19] V. Przyjalkowski, C. Shramov, “Laurent phenomenon for Landau–Ginzburg models of complete intersections in Grassmannians of planes”, Bull. Korean Math. Soc., 54:5 (2017), 1527–1575

[20] V. V. Przhiyalkovskii, K. A. Shramov, “O slabykh modelyakh Landau–Ginzburga dlya polnykh peresechenii v grassmanianakh”, UMN, 69:6 (420) (2014), 181–182 | DOI | MR | Zbl

[21] V. V. Przhiyalkovskii, K. A. Shramov, “Fenomen Lorana dlya modelei Landau–Ginzburga polnykh peresechenii v grassmanianakh”, Sovremennye problemy matematiki, mekhaniki i matematicheskoi fiziki, Tr. MIAN, 290, MAIK, M., 2015, 102–113 | DOI | MR | Zbl

[22] T. Coates, A. Kasprzyk, T. Prince, “Four-dimensional Fano toric complete intersections”, Proc. R. Soc. A, 471:2175 (2015), 20140704 | DOI | MR | Zbl

[23] C. Doran, A. Harder, “Toric Degenerations and the Laurent polynomials related to Givental's Landau–Ginzburg models”, Canad. J. Math., 68:4 (2016), 784–815 | DOI | MR | Zbl

[24] V. Przyjalkowski, “Hori–Vafa mirror models for complete intersections in weighted projective spaces and weak Landau–Ginzburg models”, Cent. Eur. J. Math., 9:5 (2011), 972–977 | DOI | MR | Zbl

[25] V. Przyjalkowski, C. Shramov, Nef Partitions for Codimension 2 Weighted Complete Intersections, 2017, arXiv: 1702.00431