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

Xie, Qihong

Asian J. Math. 9, No. 1, 121-132 (2005).

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 \(q(X) = 1\).

Reviewer: Edoardo Ballico (Povo)

MSC:

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

Keywords:

terminal variety; numerical canonical dimension; anticanonical numerical dimension