Geometry of Obstructed Equisingular Families of Algebraic Curves and Hypersurfaces
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چکیده
One of the main achievements of the algebraic geometry of the 20th century was to realize that it is fruitful not only to study algebraic varieties by themselves but also in families. That means that one should consider the space classifying all varieties with given properties. These spaces are called moduli spaces. The advantage of algebraic geometry is that many times those spaces are themselves algebraic varieties or schemes, and hence the same methods of algebraic geometry can be used to study these moduli spaces. One of the first moduli spaces considered in algebraic geometry were families of algebraic curves with given invariants and given set of singularity types. Already in the end of the 19th century, the foundation was in the works of Plücker, Severi, Segre and Zariski. Later, the theory of equisingular families had found important applications in the singularity theory, the topology of complex algebraic curves and surfaces, and in real algebraic geometry. This thesis is devoted to the study of the so-called obstructed families of plane curves, and, more generally, projective hypersurfaces, of a given degree, having one isolated singularity of prescribed type. Let Σ be a smooth projective variety over the complex field C.
منابع مشابه
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تاریخ انتشار 2008