A flop formula for Donaldson–Thomas invariants

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.