3 problems

Reid's conjecture. Under these hypotheses,

Complex-structure conjecture for $Z(m,g)$. Although for the remaining values of $g$ there are complex manifolds in the homeomorphism type of $Z(m,g)$, no $Z(m,g)$ supports a comple…

We work over the complex numbers. Let $X$ be a simply connected smooth minimal projective surface of general type, and write $K_X^2$ for the self-intersection of its canonical divi…