关于无穷小Terracini引理
On the infinitesimal Terracini lemma
摘要：
在本文中，我们证明了一个无穷小版本的经典Terracini引理3-割线平面的各种。精确地证明了：如果$X\subseteq \PP^r$是维数为$n$的不可约的、非退化的、射影复簇，且维数为$r\geq 3n+2$，使得$X$中曲线的密切平面簇具有期望维数$3n$，且对每个$0$ -维，$X$中包含一个长度为3的曲线格式$γ$，沿$γ$奇异的$X$的超平面截面族维数较大即$r-3(n+1)$，则$X$是$2$ --正割亏格。
英文摘要：
In this paper we prove an infinitesimal version of the classical Terracini Lemma for 3--secant planes to a variety. Precisely we prove that if $X\subseteq \PP^r$ is an irreducible, non--degenerate, projective complex variety of dimension $n$ with $r\geq 3n+2$, such that the variety of osculating planes to curves in $X$ has the expected dimension $3n$ and for every $0$--dimensional, curvilinear scheme $γ$ of length 3 contained in $X$ the family of hyperplanes sections of $X$ which are singular along $γ$ has dimension larger that $r-3(n+1)$, then $X$ is $2$--secant defective.
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