正规代数曲面的正则模型中缺少什么？
What is missing in canonical models for proper normal algebraic surfaces?
摘要：
光滑曲面有双生成的正则环和射影正则模型。然而，对于正规曲面，多标准截面的分次环可能是非诺特的，使得相应的齐次谱是非紧的。通过在无穷远点上增加1000个非Q-Gorenstein点，构造了一个正则紧化，条件是每个Weil因子在数值等价于一个Q-Cartier因子.类似的结果适用于任意的Weil因子，而不是典型的类。
英文摘要：
Smooth surfaces have finitely generated canonical rings and projective canonical models. For normal surfaces, however, the graded ring of multicanonical sections is possibly nonnoetherian, such that the corresponding homogeneous spectrum is noncompact. I construct a canonical compactification by adding finitely many non-Q-Gorenstein points at infinity, provided that each Weil divisor is numerically equivalent to a Q-Cartier divisor. Similar results hold for arbitrary Weil divisors instead of the canonical class.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
