On the hyperplane conjecture for periods of Calabi-Yau hypersurfaces in   $\mathbb P^n$
  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. 
Bong H. Lian, Minxian Zhu
math.AG math-ph math.MP