Some algebraicity criteria for singular surfaces
Some algebraicity criteria for singular surfaces
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奇异曲面的一些代数准则
DOI：
10.1007/bf01418372
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发表时间：
1977
影响因子：
3.1
通讯作者：
L. Brenton
中科院分区：
文献类型：
--
作者：
L. Brenton
所谓（复解析）曲面，我们指的是既约不可约的二维复空间（X，~ x），有或没有奇点。我们想知道什么时候这样的曲面是射影代数的。假设X是非奇异的。然后，我们有我们的处置分类的二维紧凑复流形主要由于科代拉（[8]）。事实上，科代拉的分类基本上是基于某些标准的代数涉及等数值不变量的贝蒂数，不规则性和几何属，超越度的亚纯函数领域。由于这些不变量在具有奇点的紧致空间中同样自然，而且常常同样容易获得，因此很自然地要问分类理论的思想在多大程度上延伸到所有（可能是奇异的）复杂曲面的更大类。在积极的一面，我们有，例如，格劳尔特的重要延伸的结果科代拉，霍奇流形是代数：
By a (complex analytic) surface we shall mean a reduced irreducible twodimensional complex space (X,~ x), with or without singularities. We want to know when such a surface is projective algebraic. Suppose X is non-singular. Then we have at our disposal the classification of two-dimensional compact complex manifolds due principally to Kodaira ([8]). Indeed, Kodaira's classification is substantially based upon certain criteria for algebraicity involving such numerical invariants as the Betti numbers, the irregularity and geometric genus, and the transcendence degree of the meromorphic function field. Since these invariants are equally natural and often equally accessible in the case of compact spaces with singular points it is natural to ask how far the ideas of the classification theory extend to the larger class of all (possibly singular) complex surfaces. On the positive side we have, for instance, Grauert's important extension of the result of Kodaira that a Hodge manifold is algebraic: