一般型光滑加权完全交的Hodge层的极大性
Hodge level and effective non-vanishing for smooth weighted complete intersections
- Steklov Mathematical Institute of Russian Academy of Sciences（俄罗斯科学院斯捷克洛夫数学研究所）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文证明一般型光滑良形加权完全交的Hodge数$h^{0,n}$为正，即Hodge层极大，并给出几何亏格下界，唯一例外是$X_{6,6}\subset\mathbb{P}(1,2,2,3,3)$。
AI中文摘要：
我们证明，对于每个维数$n>0$的一般型光滑良形加权完全交$X$，Hodge数$h^{0,n}(X)$为正；换言之，其Hodge层是极大的。我们还得到了几何亏格$p_g(X)$的一个显式下界。这意味着，唯一不是与线性锥的数值交且满足$p_g(X)=1$的一般型加权完全交是$X_{6,6}\subset\mathbb{P}(1,2,2,3,3)$。
英文摘要：
We prove that for every smooth well formed weighted complete intersection of general type of dimension $n>0$, the Hodge number $h^{0,n}(X)$ is positive; in other words, its Hodge level is maximal. We also obtain an explicit lower bound for the geometric genus $p_g(X)$. This implies that the only weighted complete intersection of general type that is not a numerical intersection with a linear cone with $p_g(X)=1$ is $X_{6,6}\subset\mathbb{P}(1,2,2,3,3)$. We also prove the Ambro--Kawamata effective non-vanishing conjecture for smooth well formed weighted complete intersections.
