The Pandharipande-Thomas rationality conjecture for superpositive curve classes on projective complex 3-manifolds

Reginald Anderson, Dominic Joyce

Let $X$ be a projective complex 3-manifold. An effective curve class ${\hat{I}}^2\in H_2(X,\mathbb{Z})$ is called positive if $c_1(X)\cdot {\hat{I}}^2>0$, and superpositive if all the effective summan…