Manifolds covered by lines, defective manifolds and a restricted Hartshorne Conjecture
Manifolds covered by lines, defective manifolds and a restricted Hartshorne Conjecture
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被线覆盖的流形、有缺陷的流形和受限的哈特肖恩猜想
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发表时间：
2009
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影响因子：
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通讯作者：
F. Russo
中科院分区：
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作者：
Paltin Ionescu;F. Russo
由小次方程定义的小的共维嵌入流形是Fano，并被线覆盖。它们是完全交点，只有当直线经过一个一般点的变化是这样的，并且有正确的余维。这使得我们可以证明二次方程流形的Hartshorne猜想，并得到这样的Hartshorne流形的列表。利用经过一般点的直线变化的几何性质，刻画了对偶缺陷流形中的涡旋。这导致了双缺陷的最优界，这改善了由于Ein的结果。讨论了具有循环Picard群的对偶缺陷流形也是割线缺陷流形的猜想，它是一种非常特殊的类型，即局部二次元轨迹变化。
Small codimensional embedded manifolds defined by equations of small degree are Fano and covered by lines. They are complete intersections exactly when the variety of lines through a general point is so and has the right codimension. This allows us to prove the Hartshorne Conjecture for manifolds defined by quadratic equations and to obtain the list of such Hartshorne manifolds. Using the geometry of the variety of lines through a general point, we characterize scrolls among dual defective manifolds. This leads to an optimal bound for the dual defect, which improves results due to Ein. We discuss our conjecture that every dual defective manifold with cyclic Picard group should also be secant defective, of a very special type, namely a local quadratic entry locus variety.
高维代数几何，2018年3月12-16日，东京大学研究生院数学科学研究生院大讲堂
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发表时间：
2018
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