Constant Scalar Curvature Kähler Surfaces and Parabolic Polystability
Constant Scalar Curvature Kähler Surfaces and Parabolic Polystability
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恒定标量曲率凯勒曲面和抛物线多稳定性
DOI：
10.1007/s12220-008-9053-8
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发表时间：
2007
影响因子：
1.1
通讯作者：
M. Singer
中科院分区：
文献类型：
--
作者：
Yann Rollin;M. Singer
一个复杂的直纹曲面允许一个由有理权抛物线结构编码的迭代爆破。在抛物线稳定的条件下，根据Rollin和Singer(J.EUR.数学课。Soc.，2004)。我们将这一结构推广到抛物多稳直纹曲面的情形。因此，我们可以产生许多具有圆或圆对称的常标量曲率的Kähler曲面的例子。
A complex ruled surface admits an iterated blow-up encoded by a parabolic structure with rational weights. Under a condition of parabolic stability, one can construct a Kähler metric of constant scalar curvature on the blow-up according to Rollin and Singer (J. Eur. Math. Soc., 2004). We present a generalization of this construction to the case of parabolically polystable ruled surfaces. Thus, we can produce numerous examples of Kähler surfaces of constant scalar curvature with circle or toric symmetry.