Download Geradenkonfigurationen und algebraische Flächen by Gottfried Barthel, Friedrich Hirzebruch, Thomas Höfer PDF
By Gottfried Barthel, Friedrich Hirzebruch, Thomas Höfer
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E. generated by global sections) line bundle over X. 1) Let L be a line bundle over X. We say that L is big if Cl (L)n > O. We say that L is neJif Cl (L) . [C] ~ 0, for all effective curves C on X. We say that L is semi-ample if there exists an m > 0, such that BslmLI, the base locus of ImLI, is empty. 2) Definition. (reduction and minimal pair) Let (X', L') be a polarized manifold. A reduction of (X' , L') is a polarized manifold (X, L) such that: a) there exists a morphism 7r : X' - X expressing X' as X with a finite set F in X blown up, b) L = 7r*(L') 0 [7r- l (F)]-l or equivalently Kx 0 Ln-l = 7r*(Kx' 0 L'n-l), c) if in addition to (a) and (b), 7r(L') = L = [8], where 8 is a minimal model of 8', where L = [8], then (X, L) is called a minimal pair.
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