On the hyperplane conjecture for periods of Calabi-Yau hypersurfaces in $\mathbb P^n$

TL;DR

This paper proves a conjecture relating solutions of hypergeometric equations to periods of Calabi-Yau hypersurfaces specifically in projective space, advancing understanding in algebraic geometry and mirror symmetry.

Contribution

It confirms the hyperplane conjecture for Calabi-Yau hypersurfaces in projective space, a case previously unverified, linking hypergeometric solutions to geometric periods.

Findings

Confirmed the conjecture for $P^n$

Established correspondence between hypergeometric solutions and periods

Enhanced understanding of Calabi-Yau hypersurfaces in toric varieties

Abstract

In [HLY1], Hosono, Lian, and Yau posed a conjecture characterizing the set of solutions to certain Gelfand-Kapranov-Zelevinsky hypergeometric equations which are realized as periods of Calabi-Yau hypersurfaces in a Gorenstein Fano toric variety $X$. We prove this conjecture in the case where $X$ is a complex projective space.