2000 character limit reached
On singular log Calabi-Yau compactifications of Landau-Ginzburg models (2102.01388v3)
Published 2 Feb 2021 in math.AG
Abstract: We consider the procedure that constructs log Calabi-Yau compactifications of weak Landau-Ginzburg models of Fano varieties. We apply it for del Pezzo surfaces and coverings of projective spaces of index one. For the coverings of degree greater then 2 the log Calabi-Yau compactification is singular; moreover, no smooth projective log Calabi-Yau compactification exists. We also prove in the cases under consideration the conjecture saying that the number of components of the fiber over infinity %and of finite fibers is equal to the dimension of an anticanonical system of the Fano variety.