Classifying birationally commutative projective surfaces
Classifying birationally commutative projective surfaces
复制标题
对双有理交换射影面进行分类
DOI：
10.1112/plms/pdq054
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发表时间：
2009
影响因子：
1.8
通讯作者：
S. Sierra
中科院分区：
文献类型：
--
作者：
S. Sierra
设R=⊕n⩾0RN是代数闭域上Gelfand-Kirillov维为3的Noether连通分次域.设R的分次商环的形式为QGR(R)≅K[z，z−1；σ]，其中K是域，我们称R是一个双交换射影曲面。我们对双交换射影曲面进行了分类，并证明了它们可以分为四类，并用几何数据进行了参数化。这推广了Rogalski和Stafford关于1次生成的双交换射影曲面的工作；我们的证明技巧是非常不同的。
Let R=⊕n⩾0Rn be a Noetherian connected graded domain of Gelfand–Kirillov dimension 3 over an algebraically closed field. Suppose that the graded quotient ring of R is of the form Qgr(R)≅K[ z,z−1;σ ], where K is a field; we say that R is a birationally commutative projective surface. We classify birationally commutative projective surfaces and show that they fall into four families, parameterized by geometric data. This generalizes the work of Rogalski and Stafford on birationally commutative projective surfaces generated in degree 1; our proof techniques are quite different.