The Crepant Transformation Conjecture implies the Monodromy Conjecture

TL;DR

This paper demonstrates that the crepant transformation conjecture for Lawrence toric DM stacks implies the monodromy conjecture for wall crossings in hypertoric stacks, linking two significant conjectures in algebraic geometry.

Contribution

It establishes a logical implication from the crepant transformation conjecture to the monodromy conjecture in the context of hypertoric stacks.

Findings

Proves the implication between the two conjectures for specific stacks.

Connects wall crossing phenomena with crepant transformations.

Provides a new perspective on the relationship between different conjectures.

Abstract

In this note we prove that the crepant transformation conjecture for a crepant birational transformation of Lawrence toric DM stacks studied in \cite{CIJ} implies the monodromy conjecture for the associated wall crossing of the symplectic resolutions of hypertoric stacks, due to Braverman, Maulik and Okounkov.