We continue in this chapter our exposition of background results with a much more specific purpose. We will concentrate on basically one object, whose construction dates back to Grothendieck in 1962: the space parametrizing curves on a given variety, or more precisely morphisms from a given smooth projective curve C to a given smooth quasi-projective variety. Mori’s techniques, which will be discussed in the next chapter, make systematic use of these spaces in a rather exotic way.
KeywordsExact Sequence Projective Space Tangent Space Irreducible Component Smooth Projective Curve
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