Laurent phenomenon for Landau--Ginzburg models of complete intersections in Grassmannians of planes

Victor Przyjalkowski; Constantin Shramov

doi:10.4134/BKMS.b160678

Bulletin of the
Korean Mathematical Society BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2017; 54(5): 1527-1575

Online first article July 3, 2017 Printed September 30, 2017

https://doi.org/10.4134/BKMS.b160678

Laurent phenomenon for Landau--Ginzburg models of complete intersections in Grassmannians of planes

Victor Przyjalkowski, Constantin Shramov

Steklov Mathematical Institute of Russian Academy of Sciences, Steklov Mathematical Institute of Russian Academy of Sciences

Abstract

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Abstract

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.

Keywords: complete intersections, Grassmannians, Landau-Ginzburg models

MSC numbers: 14E05, 14M15