Mirror Symmetry for Hypersurfaces in Weighted Projective Space and Topological Couplings

TL;DR

This paper uses toric geometry to analyze hypersurfaces in weighted projective space, computing their topological couplings and confirming mirror symmetry predictions in the large complex structure limit.

Contribution

It provides a method to compute topological couplings of hypersurfaces in weighted projective spaces and verifies mirror symmetry predictions for these models.

Findings

Topological couplings match between original and mirror models.

Toric geometry effectively computes invariants of hypersurfaces.

Results support mirror symmetry in the context of weighted projective hypersurfaces.

Abstract

By means of toric geometry we study hypersurfaces in weighted projective space of dimension four. In particular we compute for a given manifold its intrinsic topological coupling. We find that the result agrees with the calculation of the corresponding coupling on the mirror model in the large complex structure limit.