Calabi-Yau compactifications of toric Landau-Ginzburg models for smooth Fano threefolds

Abstract

We prove that smooth Fano threefolds have toric Landau--Ginzburg models. More precise, we prove that their Landau--Ginzburg models, presented as Laurent polynomials, admit compactifications to families of K3 surfaces, and we describe their fibers over infinity. We also give an explicit construction of Landau--Ginzburg models for del Pezzo surfaces and any divisors on them.

18 pages; some minor improvements are made and some misprints are corrected

References in corpus (2)

• Minkowski Polynomials and Mutations
• Hori--Vafa mirror models for complete intersections in weighted projective spaces and weak Landau--Ginzburg models

Cited by in corpus (6)

• Katzarkov-Kontsevich-Pantev Conjecture for Fano threefolds
• Hodge level for weighted complete intersections
• Calabi-Yau threefolds fibred by high rank lattice polarized K3 surfaces
• Modularity of Landau-Ginzburg models
• Threefolds Fibred by Mirror Sextic Double Planes
• G-coregularity of del Pezzo surfaces