On a numerical criterion for Fano fourfolds

Haidong Liu

On a numerical criterion for Fano fourfolds

Algebraic Geometry 2023-05-10 v3

Authors: Haidong Liu

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 $c^2_1(X)\cdot c_2(X)\neq 0$ and strictly nef anti-canonical divisor $-K_X$ is a Fano fourfold. To this aim, we completely solve the non-vanishing conjecture for strictly nef anti-canonical divisors in dimension 4.

Keywords

fano varieties nef and ample line bundles

Cite

@article{arxiv.2112.12412,
  title  = {On a numerical criterion for Fano fourfolds},
  author = {Haidong Liu},
  journal= {arXiv preprint arXiv:2112.12412},
  year   = {2023}
}

Comments

12 pages, comments are welcome. v2: we revise the introduction more clearly to show what we actually prove in this paper. v3: it is the published version, we revise the contents significantly under the suggestions of joural's referee

On a numerical criterion for Fano fourfolds

Abstract

Keywords

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