论文标题
Jacobian代数和Jacobian模块的Lefschetz属性
Lefschetz properties of Jacobian algebras and Jacobian modules
论文作者
论文摘要
让$ v：f = 0 $是复杂的投影空间中的高度$ d \ geq 3 $的超出表面。令$ m（f）$为关联的jacobian代数，$ h：\ ell = 0 $是$ \ mathbb {p}^n $中的超平面，避免了$ v $的奇异性，但是$ v \ cap h $是奇异的。我们将线性映射的Lefschetz类型属性$ \ ell：m（f）_k \ \与m（f）_ {k+1} $ to乘以线性形式$ \ ell $引起的乘法到超平面部分$ v \ cap h $的奇点。 Jacobian模块$ n（f）$也获得了类似的结果。
Let $V:f=0$ be a hypersurface of degree $d \geq 3$ in the complex projective space $\mathbb{P}^n$, $n \geq 3$, having only isolated singularities. Let $M(f)$ be the associated Jacobian algebra and $H: \ell=0$ be a hyperplane in $\mathbb{P}^n$ avoiding the singularities of $V$, but such that $V \cap H$ is singular. We related the Lefschetz type properties of the linear maps $\ell: M(f)_k \to M(f)_{k+1}$ induced by the multiplication by linear form $\ell$ to the singularities of the hyperplane section $V \cap H$. Similar results are obtained for the Jacobian module $N(f)$.
