A flop formula for Donaldson-Thomas invariants

TL;DR

This paper establishes a formula relating Donaldson-Thomas invariants of threefolds connected by a flop, revealing how these invariants transform and supporting the GW/DT correspondence under flops.

Contribution

It proves a flop formula for Donaldson-Thomas invariants of 3-folds related by a flop of disjoint (-2)-curves and proposes a conjecture for general flops.

Findings

Derived relations among BPS state counts

Showed GW/DT correspondence preservation under specific flops

Proposed a conjectural formula for general flops

Abstract

Let $X$ and $X'$ be nonsingular projective $3$-folds related by a flop of a disjoint union of $(-2)$-curves. We prove a flop formula relating the Donaldson-Thomas invariants of $X$ to those of $X'$, which implies some simple relations among BPS state counts. As an application, we show that if $X$ satisfies the GW/DT correspondence for primary insertions and descendants of the point class, then so does $X'$. We also propose a conjectural flop formula for general flops.