Computing period integrals of rigid double octic Calabi-Yau threefolds with Picard-Fuchs operator
Algebraic Geometry
2019-11-12 v2
Abstract
We present a method for numerical computation of period integrals of a rigid Calabi-Yau threefold using Picard-Fuchs operator of a one-parameter smoothing. Our method gives a possibility of computing the lattice of period integrals of a rigid double octic without any explicit knowledge of its geometric properties, employing only simple facts from the theory of Fuchsian equations and computations in MAPLE with a library for differential equations. As a surprising consequence we also get approximations of additional integrals related to a singular (nodal) model of considered Calabi-Yau threefold.
Keywords
Cite
@article{arxiv.1910.05218,
title = {Computing period integrals of rigid double octic Calabi-Yau threefolds with Picard-Fuchs operator},
author = {Tymoteusz Chmiel},
journal= {arXiv preprint arXiv:1910.05218},
year = {2019}
}