Motivic DT/PT Correspondence

TL;DR

This paper establishes a refined motivic version of the DT/PT correspondence on Calabi-Yau threefolds, combining wall crossing techniques and motivic integral identities to deepen the understanding of enumerative invariants.

Contribution

It introduces a motivic refinement of the DT/PT correspondence, integrating Toda's wall crossing framework with recent motivic integral identities.

Findings

Proves a motivic DT/PT correspondence on Calabi-Yau threefolds.

Refines the numerical DT/PT correspondence with motivic data.

Combines wall crossing and motivic integral identities for the proof.

Abstract

We prove a motivic version of the Donaldson--Thomas/Pandharipande--Thomas (DT/PT) correspondence on Calabi--Yau threefolds. The proof combines Toda's wall crossing framework and the motivic integral identity recently proved by Bu. This provides a refinement of the numerical DT/PT correspondence.