摘要翻译：
一个著名的猜想断言，光滑三元$X\子集\{\MathBB P}^5$是二次正规的，唯一的例外是Palatini卷轴。作为一个更一般陈述的推论，我们得到了与前一个猜想有关的如下结果：如果$X\子集\{\MathBB P}^5$不是二次正规的，那么它的三重曲线是可约的。对于高维变型也给出了类似的结果。
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英文标题：
《On the quadratic normality and the triple curve of three dimensional
  subvarieties of ${\mathbb P}^5$》
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作者：
Pietro De Poi, Emilia Mezzetti, Jos\'e Carlos Sierra
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最新提交年份：
2008
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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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英文摘要：
  A well-known conjecture asserts that smooth threefolds $X\subset\{\mathbb P}^5$ are quadratically normal with the only exception of the Palatini scroll. As a corollary of a more general statement we obtain the following result, which is related to the previous conjecture: If $X\subset\{\mathbb P}^5$ is not quadratically normal, then its triple curve is reducible. Similar results are also given for higher dimensional varieties.
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PDF链接：
https://arxiv.org/pdf/0811.1515