论文标题
不规则的三倍的一般类型的Noether-severi不平等和平等
Noether-Severi inequality and equality for irregular threefolds of general type
论文作者
论文摘要
我们证明了$ \ mathrm {vol}（x）（x）\ ge \ frac {4} {4} {3}χ（ω__{x}）$ for All Smooth and and smooth $ 3 $ 3 $ -folds $ -folds $ x $ type $ \ mathbb {c c} $。对于达到平等的$ 3 $ folds $ x $，我们完全描述了它们的规范模型，并表明拓扑基本组$π_1（x）\ simeq \ simeq \ mathbb {z}^2 $。作为推论，我们以相同的$ x $获得另一个最佳不等式，$ \ mathrm {vol}（x）（x）\ ge \ frac {4} {3} {3} h^0_a（x，k_x）$ withy $ h^0_a（x，k_x）$ where $ k_x $ and and and and and and and at act $ x $ x $ \ mathrm {vol}（x）= \ frac {4} {3}χ（ω__{x}）$。
We prove the optimal Noether-Severi inequality that $\mathrm{vol}(X) \ge \frac{4}{3} χ(ω_{X})$ for all smooth and irregular $3$-folds $X$ of general type over $\mathbb{C}$. For those $3$-folds $X$ attaining the equality, we completely describe their canonical models and show that the topological fundamental group $π_1(X) \simeq \mathbb{Z}^2$. As a corollary, we obtain for the same $X$ another optimal inequality that $\mathrm{vol}(X) \ge \frac{4}{3}h^0_a(X, K_X)$ where $h^0_a(X, K_X)$ stands for the continuous rank of $K_X$, and we show that $X$ attains this equality if and only if $\mathrm{vol}(X) = \frac{4}{3}χ(ω_{X})$.
