Genus one mirror symmetry for intersection of two cubics in $\mathbb{P}^5$

TL;DR

This paper proves a genus one mirror symmetry for the intersection of two cubics in projective 5-space, using toric techniques and computer calculations to determine complex invariants.

Contribution

It extends BCOV-type mirror symmetry results to a new class of Calabi-Yau threefolds, specifically intersections of two cubics in projective space.

Findings

Established genus one mirror symmetry for the intersection of two cubics in P^5

Developed computational methods using toric techniques for invariant calculation

Connected mirror symmetry predictions with explicit Gromov-Witten invariants

Abstract

This paper establishes BCOV-type genus one mirror symmetry for the intersections of two cubics in $\mathbb{P}^5$. The proof applies previous constructions of the mirror family by the second author and computations of genus one Gromov-Witten invariants by A. Popa. The approach adapts the strategy used for hypersurfaces, as developed by the first author and collaborators, but addresses the distinct geometry involved. A key feature is a systematic usage of toric techniques and related computer aided calculations to determine seemingly otherwise inaccessible invariants.