On a numerical criterion for Fano fourfolds
Abstract
In this paper, we prove a special case of Campana--Peternell's conjecture in dimension 4. Specifically, we show that a projective smooth fourfold X with c21(X)· c2(X)≠ 0 and strictly nef anti-canonical divisor -KX is a Fano fourfold. To this aim, we completely solve the non-vanishing conjecture for strictly nef anti-canonical divisors in dimension 4.
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