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摘要翻译：
研究了光滑曲面的斜坡稳定性及其与例外因子的关系。我们证明了一个包含算术亏格至少为2的例外因子的曲面对于某些极化是斜率不稳定的。在相反的方向上，我们证明了曲面的斜率稳定性可以用因子来检验，并且证明了对于非负Kodaira维数的曲面，任何失稳因子都必须具有负自交，算术亏格至少为两个。我们还证明了一个失稳因子永远不可能是nef，并作为应用给出了一个斜率稳定但不是k-稳定的曲面的例子。
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英文标题：
《Slope Stability and Exceptional Divisors of High Genus》
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作者：
Dmitri Panov and Julius Ross
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最新提交年份：
2008
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分类信息：
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
We study slope stability of smooth surfaces and its connection with exceptional divisors. We show that a surface containing an exceptional divisor with arithmetic genus at least two is slope unstable for some polarisation. In the converse direction we show that slope stability of surfaces can be tested with divisors, and prove that for surfaces with non-negative Kodaira dimension any destabilising divisor must have negative self-intersection and arithmetic genus at least two. We also prove that a destabilising divisor can never be nef, and as an application give an example of a surface that is slope stable but not K-stable.
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PDF链接：
https://arxiv.org/pdf/0710.4078
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