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

TL;DR

This paper proves that Landau-Ginzburg models for Fano complete intersections in Grassmannians are birational to complex tori, revealing a deep geometric property of these models.

Contribution

It establishes that the Landau-Ginzburg models constructed for these complete intersections are birational to complex tori, extending the understanding of their geometric structure.

Findings

Landau-Ginzburg models are birational to complex tori

Weak Landau-Ginzburg models for Fano complete intersections

Extension of Givental's construction to Grassmannians

Abstract

In 1997 Batyrev, Ciocan-Fontanine, Kim, and van Straten suggested a construction of Landau--Ginzburg models for Fano complete intersections in Grassmannians similar to Givental's construction for complete intersections in smooth toric varieties. We show that for a Fano complete intersection in Grassmannians the result of the above construction is birational to a complex torus. In other words, the complete intersections under consideration have very weak Landau--Ginzburg models.