A note on periods of Calabi--Yau fractional complete intersections

2022/04/22 by Lee, Tsung-Ju
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2204.10474

Abstract

We prove that the GKZ \mathscrD-module M_A^β arising from Calabi--Yau fractional complete intersections in toric varieties is complete, i.e., all the solutions to M_A^β are period integrals. This particularly implies that M_A^β is equivalent to the Picard--Fuchs system. As an application, we give explicit formulae of the period integrals of Calabi--Yau threefolds coming from double covers of P³ branch over eight hyperplanes in general position.

Related

• On Calabi--Yau fractional complete intersections
• Periods of double octic Calabi--Yau manifolds
• Numerical Calculation of Periods on Schoen's Class of Calabi-Yau Threefolds
• Introduction to Arithmetic Mirror Symmetry
• On periods: from global to local