Logarithmic degenerations of Landau-Ginzburg models for toric orbifolds and global tt^* geometry

Etienne Mann (1, 2) , Thomas Reichelt (3)

1 LAREMA - Laboratoire Angevin de Recherche en Mathématiques
2 IMAG - Institut Montpelliérain Alexander Grothendieck
3 Universität Heidelberg [Heidelberg] = Heidelberg University

We discuss the behavior of Landau-Ginzburg models for toric orbifolds near the large volume limit. This enables us to express mirror symmetry as an isomorphism of Frobenius manifolds which aquire logarithmic poles along a boundary divisor. If the toric orbifold admits a crepant resolution we construct a global moduli space on the B-side and show that the associated tt^*-geometry exists globally.

Domaines: Géométrie algébrique [math.AG]

Etienne Mann, Thomas Reichelt. Logarithmic degenerations of Landau-Ginzburg models for toric orbifolds and global tt^* geometry. 2023. ⟨hal-01653150⟩