 Negative-square exclusion under full sphere regularity

If every nonconstant J-holomorphic sphere under consideration is regular, no such sphere in a four-dimensional target has class $A$ with $A^2\le -2$. For a simple J-holomorphic sphere, the adjunction inequality for a simple J-holomorphic sphere makes the predicted moduli dimension negative. A degree-$m$ multiple cover of class $B$ has $B^2\le -1$ and $c_1(B)\le 1$, so its predicted real dimension is at most $2m-2$. The rational covering maps of the projective line already form a family of dimension $4m-4>2m-2$, contradicting regularity. The full regularity hypothesis matters: multiple covers of exceptional minus-one spheres violate the conclusion under a simple-only regularity assumption.