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摘要翻译：
本文研究了射影超曲面的某些阻塞等定族的几何性质，重点讨论了光滑性、可约性、可约性和维数期望。在最小阻塞性的情况下，我们给出了这类族对应于拟齐次奇点的详细描述。接下来，我们研究了这些性质关于奇点稳定等价性的行为。我们证明了在一定条件下，奇点的镇定保证了期望维数的约化分量的存在。对于最小障碍的家庭，整个家庭变得不可约。作为应用，我们证明了如果射影超曲面的等次族H具有期望维数的约化分量，则由线性系统H引起的H的变形是关于单参数变形的完全变形。
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英文标题：
《Geometry of obstructed equisingular families of projective hypersurfaces》
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作者：
Anna Gourevitch and Dmitry Gourevitch
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最新提交年份：
2009
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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 geometric properties of certain obstructed equisingular families of projective hypersurfaces with emphasis on smoothness, reducibility, being reduced, and having expected dimension. In the case of minimal obstructness, we give a detailed description of such families corresponding to quasihomogeneous singularities. Next we study the behavior of these properties with respect to stable equivalence of singularities. We show that under certain conditions, stabilization of singularities ensures the existence of a reduced component of expected dimension. For minimally obstructed families the whole family becomes irreducible. As an application we show that if the equisingular family of a projective hypersurface H has a reduced component of expected dimension then the deformation of H induced by the linear system |H| is complete with respect to one-parameter deformations.
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PDF链接：
https://arxiv.org/pdf/0803.2026
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