论文标题
Castelnuovo Bount和Gromov属的高属五重的3倍的不变性
Castelnuovo bound and higher genus Gromov-Witten invariants of quintic 3-folds
论文作者
论文摘要
我们证明了gopakumar的猜想消失结果 - 五重的3倍的VAFA不变，在文献中被称为Castelnuovo。此外，我们计算了gopakumar-castelnuovo bound $ g = \ frac {d^2+5d+10} {10} $的vafa不变。正如物理学家所表明的那样，这两种特性使我们能够计算所有的gromov - 只要对Conifold Gap条件所拥有的，五倍3倍至属的五重的五重量不变。我们还为任何一维闭合亚气管的属提供了一个平滑的高度表面$ \ leq 5 $的属，这可能具有独立的利益。
We prove a conjectural vanishing result for Gopakumar--Vafa invariants of quintic 3-folds, referred to as Castelnuovo bound in the literature. Furthermore, we calculate Gopakumar--Vafa invariants at Castelnuovo bound $g=\frac{d^2+5d+10}{10}$. As physicists showed, these two properties allow us to compute all Gromov--Witten invariants of quintic 3-folds up to genus $53$, provided that the conifold gap condition holds. We also give a bound for the genus of any one-dimensional closed subscheme in a smooth hypersurface of degree $\leq 5$, which may be of independent interest.
