Consider a smooth projective 3-fold |$X$| satisfying the Bogomolov–Gieseker conjecture of Bayer–Macrì–Toda (such as |${\mathbb{P}}^3$|⁠, the quintic 3-fold or an abelian 3-fold). Let |$L$| be a line bundle supported on a very positive surface in |$X$|⁠. If |$c_1(L)$| is a primitive cohomology class, then we show it has very negative square.

中文翻译：

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穿越墙在诺特-莱夫切茨洛奇上的应用

考虑平滑的投影三倍| $ X $ | 满足Bayer–Macrì–Toda的Bogomolov–Gieseker猜想（例如| $ {\ mathbb {P}} ^ 3 $ |⁠，五次三倍或abelian三倍）。令| $ L $ | 是| $ X $ |⁠中在非常正的表面上受支持的线束。如果| $ c_1（L）$ | 是原始的同调类，那么我们证明它具有非常负的平方。