An extension of polar duality of toric varieties and its consequences in Mirror Symmetry

Abstract

The present paper is dedicated to illustrating an extension of polar duality between Fano toric varieties to a more general duality, called framed duality, so giving rise to a powerful method of producing mirror partners of hypersurfaces and complete intersections in toric varieties, of any Kodaira dimension. In particular, the class of projective hypersurfaces and their mirror partners are studied in detail. Moreover, many connections with known Landau-Ginzburg mirror models, Homological Mirror Symmetry and Intrinsic Mirror Symmetry, are discussed.

Deformations of Calabi-Yau manifolds in Fano toric varieties

“…Therefore, it is natural to investigate whether the previous results for P n can be generalised to any toric Fano variety F , not simply P n or the smooth ones. The interest in toric Fano varieties is motivated both from the mathematics and the physics viewpoint; indeed these varieties have an essential role in the Minimal Model Program and Mirror Symmetry (see, for instance, [Ro20] for a recent work on the latter topic). In [Pe19], the author investigates deformation theory of toric Fano varieties.…”