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

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Cohomological Methods,ch as ... nef. It is then minimal in the sense that any bi-rational map from .. to a smooth projective variety is an isomorphism (Proposition 1.45). This is possible only if . is not uniruled and the (explicit) construction of .. is one of the purposes of Mori’s minimal model program.
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The Rational Quotient,l curves (so that on a rationally chain-connected variety, two general points are ℛ-equivalent). The set of ℛ-equivalence classes is not in general an algebraic variety (there exist, for example, nonruled complex projective surfaces that contain countably many rational curves!). However, Campana rea
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The Cone of Curves in the Smooth Case,tive curves. We prove here Mori’s theorem on the structure of the closure .of this cone, more exactly of the part where .. is negative. We show that it is generated by countably many ., and that these rays can only accumulate on the hyperplane .. = 0. We will give in the next chapter (§7.9) a totall
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ive faiths could be had by the dozen, when new messiahs were being unveiled in every political quarter, but when, from the relatively peaceful haven of Czechoslovakia’s First Republic, a violent struggle among them did not as yet appear imminent. Čapek’s novel, culminating in an apocalyptic war of a
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