论文标题
Kodaira尺寸为零的平滑阶乘仿射表面的分类与微不足道的单位
Classification of smooth factorial affine surfaces of Kodaira dimension zero with trivial units
论文作者
论文摘要
我们对Gurjar和Miyanishi定理进行了更正的陈述，该定理对Kodaira Dimension Zere的平滑仿射表面进行了分类，其坐标环是阶乘，并且具有微不足道的单位。用$ \ mathcal {s} _ {0} $表示此类表面的类。弗洛伊登堡（Freudenburg），小岛（Kojima）和纳加明（Nagamine）最近获得了一系列无限的表面{s} _ {0} $，未由Gurjar和Miyanishi列出。我们将它们的列表完成为一系列，其中包含$ \ Mathcal {s} _ {0} $的成对非同构表面的任意高维家族。此外，我们将它们分类为差异性，表明每种都作为4个manifold的内部，其边界是2桥结上的特殊手术。特别是，我们表明$ \ Mathcal {s} _ {0} $包含许多成对的非整形表面。
We give a corrected statement of the theorem of Gurjar and Miyanishi, which classifies smooth affine surfaces of Kodaira dimension zero, whose coordinate ring is factorial and has trivial units. Denote the class of such surfaces by $\mathcal{S}_{0}$. An infinite series of surfaces in $\mathcal{S}_{0}$, not listed by Gurjar and Miyanishi, was recently obtained by Freudenburg, Kojima and Nagamine as affine modifications of the plane. We complete their list to a series containing arbitrarily high-dimensional families of pairwise non-isomorphic surfaces in $\mathcal{S}_{0}$. Moreover, we classify them up to a diffeomorphism, showing that each occurs as an interior of a 4-manifold whose boundary is an exceptional surgery on a 2-bridge knot. In particular, we show that $\mathcal{S}_{0}$ contains countably many pairwise non-homeomorphic surfaces.
