Classification of Algebraic Varieties and Compact Complex by W. Barth, A. Van de Ven (auth.), Prof. Dr. Herbert Popp

By W. Barth, A. Van de Ven (auth.), Prof. Dr. Herbert Popp (eds.)

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Die Dimension yon R d ist nicht ganz so leicht wie (7) berechenbar. Nach dem oben Gesagten ist dimkTd(a,b) der Koeffizient von za i m Polynom n d. +z l) i=l = (l_z)-n n l+d. I ~ (1-z I) i=l also is% dimkR d nach Folgerung 1 der Koeffizient von zw in 57 (8) Yd(Z) : • (l-z) l-n - - die charakteNistische n di d wobei _%': = T ~ t i i=l n l+d. l) ~ (I- z i=l PotenzNeihe • X(~,R) : ~ dimk(Rd)i~d_ d , ist also veNboNgen in den Potenzreihe , ~(=, ! ) : X ~d(z)! ~i-~i)(i-q~)] i=l In dem speziellen Fall, dab a l l e d .

F i s t nicht normal, der singul~re Oft ist eine rationale Kurve C, die die Kurven F v o m GeschlechT 2 mit AuZ(F) a D 4 48 beschreibt. Eine weltere rationale Kurve D auf F beschreibt die Kurven F mit Aut(£) a 53 . In beiden F~llen steht hier ein Gleichheitszeichen Schnittpunkten yon C und D. Ist char k # 3,5, so schneiden sich C und D in 2 Punkten PI' P2' die der Kurve F mit Aut(F) sprechen. auSer bei den = S 4 bzw. Aut(F) = DI2 ent- £6r char k = 3 f~llt P2 fort, f~a- char k = 5 ist P1 : P2 = P mit Aut(£) = S 5.

A g a i n we use diagram W z = W ~ q-l(z) variety hypersurface. q(p-l(p(Wz))) contained in q(W) q(W) = q(p-l(p(Wz))) for all o v e r all of its points. e. q(W) ~ ~n z E q(W) is irreducible, coincides with the Schubert In the case the case that N o w for each point q(W) is , putting q(W) c G(n,k-1) has codimension 1 . 1) V . 3 , we find that an irreducible submanifold is , the n ' and it is we find q(W) is a cone is a h y p e r p l a n e cycle we again can restrict ourselves is irreducible. 1) If the variety U ~ = U ~ g-l(y) then it represents g-l(y) ~ U = f-l(v) has codimension 2 a class of bidegree G(n-k+l,1) ° We set .

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