Titlebook: Higher-Dimensional Algebraic Geometry; Olivier Debarre Textbook 2001 Springer Science+Business Media New York 2001 Dimension.Divisor.Grad.

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Curves and Divisors on Algebraic Varieties,In this preliminary chapter (as well as in the next), we gather standard material that will be used throughout the book. That is to say, material that dates mostly from pre-Mori times.

傲慢物

Parametrizing Morphisms, 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 . 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.

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,“Bend-and-Break” Lemmas, as the only smooth projective varieties with ample tangent bundle. The techniques that Mori introduced to solve this conjecture have turned out to have more far-reaching applications than Hartshorne’s conjecture itself.

背带

978-1-4419-2917-4Springer Science+Business Media New York 2001

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色情

Textbook 2001tion of algebraic varieties by proving the cone and contraction theorems..The book is well-organized and the author has kept the number of concepts that are used but not proved to a minimum to provide a mostly self-contained introduction to graduate students and researchers..

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legislate

SOB

The Cone of Curves in the Smooth Case,culations. The methods of this second proof will also give a very important additional piece of information: the existence of the contraction (see 1.16) of extremal rays on which .. is negative, which is at present unattainable by Mori’s geometric approach.

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Uniruled and Rationally Connected Varieties,ut to be equivalent, at least over an uncountable algebraically closed field: the thing that one wants to rule out is a variety not covered by rational curves say of fixed degree (with respect to some ample divisor), but which is still a (countable) union of rational curves (the degrees going to infinity).