On Pseudo-Effectivity of the Second Chern Classes for Smooth Threefolds
  We prove that for smooth projective threefolds whose anticanonical divisors are nef, the second Chern classes are pseudo-effective under a weak assumption. As an application, the pseudo-effectivity of the second Chern classes implies that Kawamata's Effective Non-vanishing Conjecture holds for such threefolds. 
Qihong Xie