A flop formula for Donaldson–Thomas invariants

Let $X$ and $X^\prime$ 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 $X^\prime$, 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 $X^\prime$. We also propose a conjectural flop formula for general flops.

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This work is partially supported by NSFC Grant 11601534, 11521101 and 11771460.

Received 4 September 2017

Accepted 21 January 2018

Published 7 June 2019