Titlebook: Geometry of Higher Dimensional Algebraic Varieties; Yoichi Miyaoka,Thomas Peternell Book 1997 Springer Basel AG 1997 Algebra.Complex analy

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Rationally Connected Fibrations and Applications structure provides us a splitting of a uniruled variety into rationally connected varieties and a non-uniruled variety. . is a natural generalization of unirationality, and in dimension two or three, we can completely characterize rationally connected varieties in terms of global holomorphic differ

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Prerequisitesmentary knowlegde on spectral sequences as found in [GH78]. There are two more advanced tools not covered by these two books which will be used over and over: the theorem of Riemann-Roch on projective manifolds (see [Ha77]) and Hironaka’s desingularisation (see Hironaka’s original paper or, for refe

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Book 1997ic p, while Part 2 is principally concerned with vanishing theorems and their geometric applications. Part I Geometry of Rational Curves on Varieties Yoichi Miyaoka RIMS Kyoto University 606-01 Kyoto Japan Introduction: Why Rational Curves? This note is based on a series of lectures given at the Mat

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Foliations and Purely Inseparable Coveringsties..What relates this new criterion of uniruledness in characteristic . to the one in characteristic zero is “semistability”. The theory of semistable torsion free sheaves will be discussed in the second section, including numerical characterizations of semistability (in characteristic zero) and i

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Abundance for Minimal 3-Foldsibration is also essential in the argument..In Section 3, the non-negativity of the Kodaira dimension of a minimal threefold is proved. The key to the proof is the pseudo-effectivity of . proved in Lecture III. We are exceptionally lucky in this case, because the Todd classes involve only . and . in

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Erhard Schütz,Jochen Vogt u. a.ties..What relates this new criterion of uniruledness in characteristic . to the one in characteristic zero is “semistability”. The theory of semistable torsion free sheaves will be discussed in the second section, including numerical characterizations of semistability (in characteristic zero) and i

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1661-237X Varieties Yoichi Miyaoka RIMS Kyoto University 606-01 Kyoto Japan Introduction: Why Rational Curves? This note is based on a series of lectures given at the Mat978-3-7643-5490-9978-3-0348-8893-6Series ISSN 1661-237X Series E-ISSN 2296-5041

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Geometry of Higher Dimensional Algebraic Varieties

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