By American Mathematical Society, János Kollár, Robert Lazarsfeld

**Read or Download Algebraic Geometry Santa Cruz 1995, Part 2: Summer Research Institute on Algebraic Geometry, July 9-29, 1995, University of California, Santa Cruz PDF**

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**Additional resources for Algebraic Geometry Santa Cruz 1995, Part 2: Summer Research Institute on Algebraic Geometry, July 9-29, 1995, University of California, Santa Cruz**

**Example text**

0 / ı rX 0 and (ii) the restriction of to X is a uniform limit of a sequence m is a semipositive model metric. m j X , where each Here 0 is a fixed model metric, determined by some model dominated by X . The map rX W X an ! X X an is a natural retraction. Since is usc, condition (i) implies that D 0 ClimX . 0 /ırX , so that is determined by its restrictions to all dual complexes. 38 S. Boucksom et al. 2 and Ascoli’s theorem. Regularization, however, is quite difficult to show. We are not aware of any procedure that would replace convolution in the complex case.

Regularization, however, is quite difficult to show. We are not aware of any procedure that would replace convolution in the complex case. Instead we use algebraic geometry. Here is an outline of the proof. Lan /. For any SNC model X , naturally induces a model metric X . The semipositivity of implies that the net . X /X indexed by the collection of (isomorphism classes of) SNC models decreases to . Unfortunately, except in the curve case n D 1, X has no reason to be semipositive; this reflects the fact that the pushforward of a nef line bundle may fail to be nef.

S / (10) Forms and Currents on the Analytification of an Algebraic Variety. . U! /s . Inserting (10) in (9) by using that the special fibre of X! Y! Y! /s / is the multiplicity of the irreducible component C in the special alg fibre of Y! By definition, the right-hand side is equal to m which proves the claim. 12. e. independent of the choice of the generic projection q. 9 gives a new proof for the classical balancing condition for tropical varieties which is based mainly on degree considerations.