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Contractions of Gorenstein polarized varieties with high nef value. (English) Zbl 0813.14009

Let \(X\) be a normal complex projective variety of dimension \(n\) with Gorenstein terminal singularities; let \(L\) be an ample line bundle over \(X\) and let \(K_ X\) denote the canonical sheaf of \(X\). Assuming that \(K_ X\) is not nef we study the contractions of extremal faces which are supported by divisors of the form \(K_ X + \tau L\) with \(\tau \geq (n- 2)\). In other words we classify the pairs \((X,L)\) which have “nef value” \(=\tau (X,L) \geq (n-2)\) as well as the structure of their associate “nef value morphisms”. In the case \(\tau = (n-2)\) we assume also that \(X\) is factorial. We study moreover the general case in which \((K_ X + \tau L)\) is nef and big but not ample and the dimension of the fibers of the nef value morphism is \(\leq r\).
Reviewer: M.Andreatta (Povo)

MSC:

14E30 Minimal model program (Mori theory, extremal rays)
14M05 Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal)
14C20 Divisors, linear systems, invertible sheaves
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References:

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