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

HPA533

Deformations and Rational CurvesIn this lecture, we give a brief account on the fundamental notions such as Hilbert schemes, Chow schemes, deformation of morphisms, and intersection pairing between curves and divisors, along with their application to the construction of rational curves on a projective variety.

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978-3-7643-5490-9Springer Basel AG 1997

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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 references and statements, [GPR94]).

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Lyrischer Ausklang der RevolutionTheory”. The construction of minimal models was discussed by T. Peternell, and my task was to give an overview of various aspects of the study of rational curves on algebraic varieties, including the following topics:

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