Positivity conjecture for fixed-domain Gromov–Witten invariants of Fano varieties

Let $X$ be a smooth Fano variety of complex dimension $r$, let $g$ be a genus, and let $A$ be a curve class. The fixed-domain Gromov–Witten invariants are the virtual counts associated with fixed marked domains and incidence constraints. Positivity conjecture. The fixed-domain Gromov–Witten invariants are positive when $\langle c_1(X),A\rangle$ is large compared to $r$ and $g$. Positivity is known in all examples discussed in the source, but the general assertion is presented as an unresolved expectation; enumerativity is explicitly distinct from positivity and can fail even in large degree.