Download Algebraic Geometry Bucharest 1982: Proceedings of the by Lucian BĂdescu (auth.), Lucian Bădescu, Dorin Popescu (eds.) PDF

By Lucian BĂdescu (auth.), Lucian Bădescu, Dorin Popescu (eds.)

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Extra info for Algebraic Geometry Bucharest 1982: Proceedings of the International Conference held in Bucharest, Romania, August 2–7, 1982

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Ann. 221 (1976) 55-72. 38. ~ ~ * , Correspondence, Amer. Math. 79 (1957) 951-952 ( - A. Wail, Oeuvres sc. II 555-556). INCREST Bucharest, Dept. of Mathematics, B-dul P~cii 220, 79622 Bucharest, Rumania. TOPOLOGICALLY BUNDLES Vasile TRIVIAL ALGEBRAIC 2-VECTOR ON RULED S U R F A C E S . I I BRINZANESCU and M a n u e l a STOIA INTRODUCTION It is a c l a s s i c a l continuous their Chern trivial complex result vector classes that on c o m p a c t bundles Cl,C 2 of rank (Wu[13]). iff Cl=0 and c2=0.

4) K=2LI+L 2 where L i are d i s t i n c t straight lines. By a d j u n c t i o n we get - 2 = 3 L ~ + L I L 2 and - 2 = 2 L ~ + 2 L I L 2. It follows that LIL2=I hence L 1 is exceptional. After c o n t r a c t i n g L 1 one sees that the image of L 2 be- comes also exceptional. This s i t u a t i o n leads to case III3c. 5) K is the sum of three d i s t i n c t s t r a i g h t lines. By a d j u n c t i o n again, we get that either the lines are d i s j o i n t and e x c e p t i o n a l (in w h i c h case we are led to type III3d) or they are c o p l a n a r with s e l f i n t e r s e c t i o n s -2 (in w h i c h case X is minimal w i t h K2=0, hence x must be of type III3e).

In the case of tile rational ruled surface x=F1 for M(1,1) we have:Po=pic°c=one point, deg Y=I, hence the Hilbert variety H°=FI , the universal subspace y is the diagonal A and dim Ext~ (Iy,L2~i~l)=l. It X follows that the variety Z consists of a single stratum and M(I,I)=FI. The previous diagram becomes: id. Fp Fl ~> Fl× Fl IP Fi We have ~-P2 id. I~T~OCO~ ± ~ r z1× r z~' -) F1 but ExitI(IA~TI,T 2)=Ext 2 (OA~T I,T2))= coFz"F1=P*l(coFz )~P~ (coF), 1 coF/°F1 (-2Co-3fo), TI-P I - * (OEI. (-Co-f o)), T2=P l(OFz (Co+f 0)) and by means of the identification A=FI we get R=OFl(4co+5fo).

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