论文标题
在无穷小的陶土引理上
On the infinitesimal Terracini lemma
论文作者
论文摘要
在本文中，我们证明了3-秒飞机的经典陶器引理的无限版本。确切地说，如果 $X\subseteq \PP^r$ 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 $ x $的部分沿$γ$具有$ r-3（n+1）$的尺寸，然后$ x $为$ 2 $ - secant有缺陷。
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.
