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摘要翻译：
证明了在$\MathBB{P}^5$中存在两个新的局部Cohen-Macaulay六次三元族，它们不是二次正规的。这三个方面在作为焦点轨迹的直线的一阶同余领域和完全例外的Monge-Amp\'ere方程的研究中自然出现。这些族中的一个来自于多次$(1,3,3)$的光滑同余，它是指数2和属9的光滑Fano的四倍。
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英文标题：
《Congruences of lines in $\mathbb{P}^5$, quadratic normality, and
completely exceptional Monge-Amp\`ere equations》
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作者：
Pietro De Poi and Emilia Mezzetti
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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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英文摘要：
The existence is proved of two new families of locally Cohen-Macaulay sextic threefolds in $\mathbb{P}^5$, which are not quadratically normal. These threefolds arise naturally in the realm of first order congruences of lines as focal loci and in the study of the completely exceptional Monge-Amp\`ere equations. One of these families comes from a smooth congruence of multidegree $(1,3,3)$ which is a smooth Fano fourfold of index two and genus 9.
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PDF链接：
https://arxiv.org/pdf/0710.5110
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