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摘要翻译：
给出了有限域上光滑射影簇上的nef线丛的第一个例子，它不是半充分的。更具体地说，我们在有限域上的光滑射影曲面上找到了光滑曲线，使得法丛具有零度，但在不相交曲线族中没有曲线的正倍数移动。这回答了基尔和芒福德的问题。这个证明使用了障碍理论，本着同伦理论的精神，它将无限多的障碍与给定的余维一次变体的越来越高的倍数联系起来。在有限域上的3-折叠上，我们发现了nef和不是半满的大线丛。最后，我们对有限域上半放大的一些已知的正结果进行了反驳。
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英文标题：
《Moving codimension-one subvarieties over finite fields》
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作者：
Burt Totaro
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最新提交年份：
2007
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分类信息：
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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一级分类：Mathematics 数学
二级分类：Number Theory 数论
分类描述：Prime numbers, diophantine equations, analytic number theory, algebraic number theory, arithmetic geometry, Galois theory
素数，丢番图方程，解析数论，代数数论，算术几何，伽罗瓦理论
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英文摘要：
We give the first examples of nef line bundles on smooth projective varieties over finite fields which are not semi-ample. More concretely, we find smooth curves on smooth projective surfaces over finite fields such that the normal bundle has degree zero, but no positive multiple of the curve moves in a family of disjoint curves. This answers questions by Keel and Mumford. The proof uses an obstruction theory, in the spirit of homotopy theory, which links the infinitely many obstructions to moving higher and higher multiples of a given codimension-one subvariety. On 3-folds over a finite field, we find nef and big line bundles which are not semi-ample. Finally, we reprove some of the known positive results about semi-ampleness over finite fields.
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PDF链接：
https://arxiv.org/pdf/0712.2049
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