论文标题
关于投影空间中曲线一般工会的希尔伯特功能
On the Hilbert function of general unions of curves in projective spaces
论文作者
论文摘要
令$ x = x_1 \ cup \ cdots \ cup x_s \ subset \ subset \ mathbb {p}^n $，$ n \ ge 4 $，成为平滑的非特殊曲线的一般结合，$ x_i $ $ x_i $ of $ d_i $和genus $ g_i $和$ g_i $和$ d_i \ ge \ ge \ ge \ ge \ ge \ ge \ ge \ ge \ ge \ max \ nif \ nif \ n \ n \ n \ n \ n \最大c_i \ n \ nif $ g_i> 0 $。我们证明$ x $具有最大排名，即对于任何$ t \ in \ athbb {n} $ $ h^0（\ nathcal {i} _x（t））= 0 $或$ h^1（\ mathcal {\ mathcal {i} _x（i} _x（t））= 0 $。
Let $X=X_1\cup \cdots \cup X_s\subset \mathbb {P}^n$, $n\ge 4$, be a general union of smooth non-special curves with $X_i$ of degree $d_i$ and genus $g_i$ and $d_i\ge \max \{2g_i-1,g_i+n\}$ if $g_i>0$. We prove that $X$ has maximal rank, i.e. for any $t\in \mathbb {N}$ either $h^0(\mathcal{I}_X(t))=0$ or $h^1(\mathcal{I}_X(t))=0$.
