Shifting local exponents of Picard-Fuchs operators

TL;DR

This paper explores how shifting local exponents affects the monodromy of Calabi-Yau threefold families, characterizing geometric shifts and constructing operators with unique properties.

Contribution

It provides a characterization of geometric shifts of local exponents in Picard-Fuchs operators and constructs operators with novel properties.

Findings

Characterization of geometric shifts of local exponents

Construction of Picard-Fuchs operators with interesting properties

Insights into monodromy representations of Calabi-Yau families

Abstract

We investigate the operation of shifting local exponents and study its effects on the monodromy representation of a one-parameter family of Calabi-Yau threefolds. The main result is a characterization of shifts of geometric operators which are also geometric. We use this description to construct some Picard-Fuchs operators with interesting properties.