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摘要翻译：
在Fine和Song-Tian的著作中，我们引入了一个上同调障碍来求解以半正形式扭转的常数标量曲率K\\Ahler(cscK)方程。这在几何上给出了一个障碍，使流形成为在某些绝热类中携带cscK度量的全纯淹没的基，从而产生了许多不允许cscK代表的一般三元数的新例子。当扭转消失时，我们的障碍将Ross-Thomas的斜率稳定性推广到K\\Ahler流形上的有效因子。因此，我们找到了非射影斜率不稳定流形的例子。
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英文标题：
《Twisted cscK metrics and K\"ahler slope stability》
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作者：
Jacopo Stoppa
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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：Differential Geometry 微分几何
分类描述：Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis
复形，接触，黎曼，伪黎曼和Finsler几何，相对论，规范理论，整体分析
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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 introduce a cohomological obstruction to solving the constant scalar curvature K\"ahler (cscK) equation twisted by a semipositive form, appearing in works of Fine and Song-Tian. Geometrically this gives an obstruction for a manifold to be the base of a holomorphic submersion carrying a cscK metric in certain ``adiabatic'' classes. In turn this produces many new examples of general type threefolds with classes which do not admit a cscK representative. When the twist vanishes our obstruction extends the slope stability of Ross-Thomas to effective divisors on a K\"ahler manifold. Thus we find examples of non-projective slope unstable manifolds.
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PDF链接：
https://arxiv.org/pdf/0804.0414
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