强度与高次Hartshorne猜想
Strength and Hartshorne's Conjecture in high degree
摘要：
Hartshorne证明了n维射影空间的一个光滑的余维c子流形必须是一个完全的交集，只要c小于n/3。我们证明了这一点的特殊情况下，当n是远远大于程度的子品种。类似的结果是已知的特征零由于哈特霍恩，巴特-范德文，和其他人。我们的证明是领域独立的，并采用完全不同的方法从以前的结果，因为我们连接Hartshorne的猜想与循环的想法发起的Ananyan和Hochster在他们的证明斯蒂尔曼猜想。
英文摘要：
Hartshorne conjectured that a smooth, codimension c subvariety of n-dimensional projective space must be a complete intersection, whenever c is less than n/3. We prove this in the special case when n is much larger than the degree of the subvariety. Similar results were known in characteristic zero due to Hartshorne, Barth-Van de Ven, and others. Our proof is field independent and employs quite different methods from those previous results, as we connect Hartshorne's Conjecture with the circle of ideas initiated by Ananyan and Hochster in their proof of Stillman's Conjecture.
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