We give a reduction of the conjecture that for terminal projective threefolds whose anticanonical divisors are nef, the second Chern classes are pseudo-effective. On the other hand, some effective non-vanishing results are obtained as applications of the pseudo-effectivity of the second Chern classes.
"On Pseudo-Effectivity of the Second Chern Classes for Terminal Threefolds." Asian J. Math. 9 (1) 121 - 132, March, 2005.