This publication is predicated on lecture notes of a seminar of the Deutsche Mathematiker Vereinigung held via the authors at Oberwolfach from April 2 to eight, 1995. It supplies an creation to the category thought and geometry of upper dimensional complex-algebraic types, concentrating on the tremendeous advancements of the sub­ ject within the final twenty years. The paintings is in components, with each preceeded by way of an creation describing its contents intimately. right here, it's going to suffice to easily ex­ undeniable how the subject material has been divided. Cum grano salis one may well say that half 1 (Miyaoka) is extra inquisitive about the algebraic equipment and half 2 (Peternell) with the extra analytic points although they've got unavoidable overlaps simply because there's no clearcut contrast among the 2 tools. in particular, half 1 treats the deformation conception, life and geometry of rational curves through attribute p, whereas half 2 is especially desirous about vanishing theorems and their geometric purposes. half I Geometry of Rational Curves on forms Yoichi Miyaoka RIMS Kyoto college 606-01 Kyoto Japan creation: Why Rational Curves? This be aware relies on a sequence of lectures given on the Mathematisches Forschungsin­ stitut at Oberwolfach, Germany, as part of the DMV seminar "Mori Theory". the development of minimum types was once mentioned via T.

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