## On pseudo-effectivity of the second Chern classes for terminal threefolds.(English)Zbl 1083.14009

Let $$X$$ be a terminal projective threefold with $$-K_X$$ nef. Is the second Chern class $$c_2(X)$$ pseudoeffective? Here the author proves this conjecture if something else is true. This reduction allows the author to prove several non-vanishing theorems. Here there is one of them; let $$X$$ be a canonical projective threefold such that $$-K_X$$ is nef; let $$\nu (-K_X)$$ denote the numerical dimension of the anticanonical sheaf; the effective non-vanishing holds on $$X$$ if either $$\nu (-K_X) \neq 2$$ or $$\nu (-K_X)=2$$ and $$q(X) = 1$$.

### MSC:

 14C17 Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry 14E30 Minimal model program (Mori theory, extremal rays) 14J30 $$3$$-folds
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