Acknowledgement
Supported by : Russian Science Foundation
References
- L. Aizenberg, A. Tsikh, and A. Yuzhakov, Higher-dimensional residues and their applications, Current problems in mathematics, Fundamental directions, Vol. 8, 5-64, 274, Itogi Nauki i Tekhniki, Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow, 1985.
- V. V. Batyrev, Toric degenerations of Fano varieties and constructing mirror manifolds, The Fano conference, pp. 109-122, Univ. Torino, Turin, 2004.
- V. V. Batyrev, I. Ciocan-Fontanine, B. Kim, and D. van Straten, Conifold transitions and mirror symmetry for Calabi{Yau complete intersections in Grassmannians, Nucl. Phys. B 514 (1998), no. 3, 640-666. https://doi.org/10.1016/S0550-3213(98)00020-0
- V. V. Batyrev, I. Ciocan-Fontanine, B. Kim, and D. van Straten, Mirror symmetry and toric degenerations of partial ag manifolds, Acta Math. 184 (2000), no. 1, 1-39. https://doi.org/10.1007/BF02392780
- A. Bertram, I. Ciocan-Fontanine, and B. Kim, Two Proofs of a Conjecture of Hori and Vafa, Duke Math. J. 126 (2005), no. 1, 101-136. https://doi.org/10.1215/S0012-7094-04-12613-2
- T. Coates, A. Corti, S. Galkin, V. Golyshev, and A. Kasprzyk, Mirror Symmetry and Fano Manifolds, European Congress of Mathematics, pp. 285-300, (Krakow, 2-7 July, 2012), November 2013.
- T. Coates, A. Kasprzyk, and T. Prince, Four-dimensional Fano toric complete intersections, Proc. R. Soc. A 471 (2015), 20140704.
- D. Cox, J. Little, and H. Schenck, Toric varieties, Graduate Studies in Mathematics 124. Providence, RI: AMS, 2011.
- O. Debarre, A. Iliev, and L. Manivel, On the period map for prime Fano threefolds of degree 10, J. Algebr. Geom. 21 (2012), no. 1, 21-59. https://doi.org/10.1090/S1056-3911-2011-00594-8
- O. Debarre, A. Iliev, and L. Manivel, Special prime Fano fourfolds of degree 10 and index 2, Recent advances in algebraic geometry. A volume in honor of Rob Lazarsfelds 60th birthday. Cambridge: CUP. LMS Lecture Note Series 417 (2014), 123-155.
- C. Doran and A. Harder, Toric Degenerations and the Laurent polynomials related to Givental's Landau-Ginzburg models, Canad. J. Math. 68 (2016), no. 4, 784-815. https://doi.org/10.4153/CJM-2015-049-2
- C. Doran, A. Harder, L. Katzarkov, J. Lewis, and V. Przyjalkowski, Modularity of Fano threefolds, in preparation.
- T. Eguchi, K. Hori, and C.-Sh. Xiong, Gravitational quantum cohomology, Internat. J. Modern Phys. A 12 (1997), no. 9, 1743-1782. https://doi.org/10.1142/S0217751X97001146
- S. Galkin, Small toric degenerations of Fano 3-folds, preprint, http://www.mi.ras.ru/-galkin/work/3a.pdf.
- A. Givental, Stationary phase integrals, quantum Toda lattices, flag manifolds and the mirror conjecture, Topics in singularity theory, 103-115, Amer. Math. Soc. Transl. Ser. 2, 180, AMS, Providence, RI, 1997.
- A. Givental, A mirror theorem for toric complete intersections, Topological field theory, primitive forms and related topics (Kyoto, 1996), 141-175, Progr. Math., 160, Birkhauser Boston, Boston, MA, 1998.
- S. O. Gorchinskiy and D. V. Osipov, A higher-dimensional Contou-Carrere symbol: local theory, Sbornik: Math. 206 (2015), no. 9, 1191-1259. https://doi.org/10.1070/SM2015v206n09ABEH004494
- S. O. Gorchinskiy and D. V. Osipov, Continuous homomorphisms between algebras of iterated Laurent series over a ring, Proc. Steklov Inst. Math. 294 (2016), 47-66. https://doi.org/10.1134/S0081543816060031
- S. O. Gorchinskiy and D. V. Osipov, Higher-dimensional Contou-Carrere symbol and continuous automorphisms, Funct. Anal. Its Appl. 50 (2016), 268-280. https://doi.org/10.1007/s10688-016-0158-8
- M. Gross, L. Katzarkov, and H. Ruddat, Towards mirror symmetry for varieties of general type, Adv. Math. 308 (2017), 208-275. https://doi.org/10.1016/j.aim.2016.03.035
- K. Hori and C. Vafa, Mirror symmetry, arXiv:hep-th/0002222.
- N. Ilten, J. Lewis, and V. Przyjalkowski, Toric degenerations of fano threefolds giving weak Landau-Ginzburg models, J. Algebra 374 (2013), 104-121. https://doi.org/10.1016/j.jalgebra.2012.11.002
- V. Iskovskikh and Yu. Prokhorov, Fano varieties, Encyclopaedia of Mathematical Sciences, 47 (1999) Springer, Berlin.
- L. Katzarkov and V. Przyjalkowski, Landau-Ginzburg models-old and new, Proceedings of the Gokova Geometry-Topology Conference 2011, 97-124, Int. Press, Somerville, MA, 2012.
- B. Kim, Quantum hyperplane section principle for concavex decomposable vector bundles, J. Korean Math. Soc. 37 (2000), no. 3, 455-461.
- M. Kontsevich, Homological algebra of mirror symmetry, Proc. International Congress of Matematicians, Vol. 1,2 (Zurich 1994), pp. 120-139, Birkhauzer, Basel, 1995.
- A. Kuznetsov, On Kuchle varieties with Picard number greater than 1, Izv. Math. 79 (2015), no. 4, 698-709. https://doi.org/10.1070/IM2015v079n04ABEH002758
- A. Kuznetsov, Kuchle fivefolds of type c5, Math. Z. 284 (2016), no. 3-4, 1245-1278. https://doi.org/10.1007/s00209-016-1707-9
- Y. Lee, Quantum Lefschetz hyperplane theorem, Invent. Math. 145 (2001), no. 1, 121-149. https://doi.org/10.1007/s002220100145
- Zh. Li, On the birationality of complete intersections associated to nef-partitions, arXiv:1310.2310.
- Yu. Manin, Frobenius manifolds, quantum cohomology, and moduli spaces, Colloquium Publications. American Mathematical Society (AMS), 47. Providence, RI: American Mathematical Society (AMS), 1999.
- R. Marsh and K. Rietsch, The B-model connection and mirror symmetry for Grassmannians, arXiv:1307.1085.
- T. Prince, Efficiently computing torus charts in Landau{Ginzburg models of complete intersections in Grassmannians of planes, Bull. Korean Math. Soc. 54 (2017), no. 5, 1719-1724. https://doi.org/10.4134/BKMS.B160688
- V. Przyjalkowski, On Landau-Ginzburg models for Fano varieties, Comm. Num. Th. Phys. 1 (2008), no. 4, 713-728. https://doi.org/10.4310/CNTP.2007.v1.n4.a4
- V. Przyjalkowski, Hori-Vafa mirror models for complete intersections in weighted projective spaces and weak Landau-Ginzburg models, Cent. Eur. J. Math. 9 (2011), no. 5, 972-977. https://doi.org/10.2478/s11533-011-0070-7
- V. Przyjalkowski, Weak Landau-Ginzburg models for smooth Fano threefolds, Izv. Math. 77 (2013), no. 4, 135-160.
- V. Przyjalkowski, Calabi-Yau compactications of toric Landau-Ginzburg models for smooth Fano threefolds, Sb. Math. 208 (2017), no. 7, DOI:10.1070/SM8838.
- V. Przyjalkowski, On Calabi-Yau compactifications of toric Landau-Ginzburg models for Fano complete intersections, Math. Notes 102 (2018), arXiv:1701.08532.
- V. Przyjalkowski and C. Shramov, Laurent phenomenon for Landau-Ginzburg models of complete intersections in Grassmannians of planes, arXiv:1409.3729. https://doi.org/10.4134/BKMS.B160678
- V. Przyjalkowski and C. Shramov, On weak Landau-Ginzburg models for complete intersections in Grassmannians, Russian Math. Surveys 69 (2014), no. 6, 1129-1131. https://doi.org/10.1070/RM2014v069n06ABEH004931
- V. Przyjalkowski and C. Shramov, On Hodge numbers of complete intersections and Landau-Ginzburg models, Int. Math. Res. Not. 2015 (2015), no. 21, 11302-11332. https://doi.org/10.1093/imrn/rnv024
- V. Przyjalkowski and C. Shramov, Laurent phenomenon for Landau-Ginzburg models of complete intersections in Grassmannians, Proc. Steklov Inst. Math. 290 (2015), no. 1, 91-102. https://doi.org/10.1134/S0081543815060097
- B. Sturmfels, Algorithms in Invariant Theory, Texts and Monographs in Symbolic Computation, Wien, Springer-Verlag, 1993.
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