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In a spirit of Givental's constructions Batyrev, Ciocan-Fonta\-nine, Kim, and van Straten suggested Landau--Ginzburg models for smoo\-th Fano complete intersections in Grassmannians and partial flag varieties as certain complete intersections in complex tori equipped with special functions called superpotentials. We provide a particular algorithm for constructing birational isomorphisms of these models for complete intersections in Grassmannians of planes with complex tori. In this case the superpotentials are given by Laurent polynomials. We study Givental's integrals for Landau--Ginzburg models suggested by Batyrev, Ciocan-Fontanine, Kim, and van Straten and show that they are periods for pencils of fibers of maps provided by Laurent polynomials we obtain. The algorithm we provide after minor modifications can be applied in a more general context.
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참고문헌 (32)
참고문헌 신청
A. Bertram / 2005 / Two Proofs of a Conjecture of Hori and Vafa / Duke Math. J 126 (1) : 101 ~ 136
A. Givental / 1997 / Topics in singularity theory / AMS : 103 ~ 115
A. Givental / 1998 / Topological field theory, primitive forms and related topics / Birkhauser Boston : 141 ~ 175
A. Kuznetsov / 2015 / On Kuchle varieties with Picard number greater than 1 / Izv. Math 79 (4) : 698 ~ 709
A. Kuznetsov / 2016 / Kuchle fivefolds of type c5 / Math. Z 284 (3-4) : 1245 ~ 1278
A. Givental / 1997 / Topics in singularity theory / AMS : 103 ~ 115
A. Givental / 1998 / Topological field theory, primitive forms and related topics / Birkhauser Boston : 141 ~ 175
A. Kuznetsov / 2015 / On Kuchle varieties with Picard number greater than 1 / Izv. Math 79 (4) : 698 ~ 709
A. Kuznetsov / 2016 / Kuchle fivefolds of type c5 / Math. Z 284 (3-4) : 1245 ~ 1278
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