论文标题
关于哈里斯的猜想
On a conjecture of Harris
论文作者
论文摘要
对于$ d \ ge 4 $，noether-lefschetz locus $ \ mathrm {nl} _d $ parametrize smooth，$ d $ d $表面$ \ mathbb {p}^3 $带有Picard号码至少$ 2 $。哈里斯的一个猜想指出，非麦克风编成的Noether-Lefschetz基因座只有有限的许多不可还原组成部分。 Voisin表明，猜想是错误的，对于足够大的$ D $，但对于$ d \ le 5 $是正确的。她还表明，对于$ d = 6，7 $，有限的许多\ emph {降低}，是$ \ mathrm {nl} _d $ non-maximal codimension的$ \ mathrm {nl} _d $。在本文中，我们证明，对于任何$ d \ ge 6 $，都有$ \ mathrm {nl} _d $ of non-maximal condimension的$ \ mathrm {nl} _d $的无限\ emph {non-reded}不可删除的组件。
For $d \ge 4$, the Noether-Lefschetz locus $\mathrm{NL}_d$ parametrizes smooth, degree $d$ surfaces in $\mathbb{P}^3$ with Picard number at least $2$. A conjecture of Harris states that there are only finitely many irreducible components of the Noether-Lefschetz locus of non-maximal codimension. Voisin showed that the conjecture is false for sufficiently large $d$, but is true for $d \le 5$. She also showed that for $d=6, 7$, there are finitely many \emph{reduced}, irreducible components of $\mathrm{NL}_d$ of non-maximal codimension. In this article, we prove that for any $d \ge 6$, there are infinitely many \emph{non-reduced} irreducible components of $\mathrm{NL}_d$ of non-maximal codimension.
