Hodge numbers of Fano threefolds via Landau--Ginzburg models

2009/11/28 by Przyjalkowski, Victor
#14D07 #14J30 #14J33 #14J45 #14M25 #14N35 #52B20 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.0911.5428

Abstract

For each smooth Fano threefold X with Picard number 1 we consider a weak Landau--Ginzburg model, that is a fibration over \mathbb C¹ given by a certain Laurent polynomial. In the spirit of L. Katzarkov's program we prove that the number of irreducible components of the central fiber of its compactification is h^1,2(X)+1. In particular, it does not depend on the compactification. The question of dependence on the model is open; however we produce examples of different weak Landau--Ginzburg models for the same variety with the same number of components of the central fiber.

Related

• Hodge numbers of Landau-Ginzburg models
• Geography of Landau-Ginzburg models and threefold syzygies
• Degenerations, fibrations and higher rank Landau-Ginzburg models
• Modularity of Landau-Ginzburg models
• Singularities of Landau-Ginzburg models for complete intersections and derived categories