论文标题
代数三倍的一般类型，体积小
Algebraic threefolds of general type with small volume
论文作者
论文摘要
众所周知，最佳NOETH不等式$ \ MATHRM {VOL}（x）\ ge \ frac {4} {3} {3} p_g（x） - \ frac {10} {3} {3} $可容纳每一个$ 3 $ -fold $ -fold $ -fold $ -fold $ -fold $ x $ the General Type tange type type $ p_g（x）\ ge ge ge 11 $ 11 $。在本文中，我们通过$ p_g（x）\ ge 11 $提供了$ 3 $ - folds $ x $的完整分类，通过提供$ x $的相对规范模型的明确结构来满足上述平等。当$ p_g（x）\ ge 23 $时，该型号与$ x $的规范模型相吻合。我们还以$ 3 $ folds $ x $的通用类型和$ p_g（x）\ ge 11 $建立了第二和第三最佳的noether不平等现象。这些结果回答了J. Chen，M。Chen和C. Jiang提出的两个空旷的问题，在Dimension三中，J。Chen和C. Lai提出了一个空旷的问题。一种新颖的现象表明，这三个Noether不平等与$ p_g（x）$ modulo $ 3 $的三个可能的残基之间有一对一的对应关系。
It is known that the optimal Noether inequality $\mathrm{vol}(X) \ge \frac{4}{3}p_g(X) - \frac{10}{3}$ holds for every $3$-fold $X$ of general type with $p_g(X) \ge 11$. In this paper, we give a complete classification of $3$-folds $X$ of general type with $p_g(X) \ge 11$ satisfying the above equality by giving the explicit structure of a relative canonical model of $X$. This model coincides with the canonical model of $X$ when $p_g(X) \ge 23$. We also establish the second and third optimal Noether inequalities for $3$-folds $X$ of general type with $p_g(X) \ge 11$. These results answer two open questions raised by J. Chen, M. Chen and C. Jiang, and in dimension three an open question raised by J. Chen and C. Lai. A novel phenomenon shows that there is a one-to-one correspondence between the three Noether inequalities and three possible residues of $p_g(X)$ modulo $3$.
