Curves disjoint from a nef divisor
Curves disjoint from a nef divisor
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曲线与 nef 除数不相交
DOI：
10.1307/mmj/1465329015
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
J. C. Ottem
中科院分区：
文献类型：
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作者：
John Lesieutre;J. C. Ottem
众所周知，在射影曲面上，与Nef线丛正交的曲线集要么是有限的，要么是不可数的。我们表明，这种二分法失败，在更高的维度，通过构建一个nef线丛的三倍，这是平凡的可数无穷多条曲线。这回答了托塔罗的一个问题。作为一个令人愉快的推论，我们展示了一个准投射品种只有一个可数无限集的完整，正维的子品种。
On a projective surface it is well-known that the set of curves orthogonal to a nef line bundle is either finite or uncountable. We show that this dichotomy fails in higher dimension by constructing a nef line bundle on a threefold which is trivial on countably infinitely many curves. This answers a question of Totaro. As a pleasant corollary, we exhibit a quasi-projective variety with only a countably infinite set of complete, positive-dimensional subvarieties.