Algebraic Surfaces by Arnaud Beauville (auth.), G. Tomassini (eds.) PDF

By Arnaud Beauville (auth.), G. Tomassini (eds.)

ISBN-10: 364211086X

ISBN-13: 9783642110863

ISBN-10: 3642110878

ISBN-13: 9783642110870

Lectures: A. Beauville: Surfaces algébriques complexes.- F.A. Bogomolov: the speculation of invariants and its purposes to a couple difficulties within the algebraic geometry.- E. Bombieri: tools of algebraic geometry in Char. P and their applications.- Seminars: F. Catanese: Pluricanonical mappings of surfaces with okay² =1,2, q=pg=0.- F. Catanese: On a category of surfaces of normal type.- I. Dolgacev: Algebraic surfaces with p=pg =0.- A. Tognoli: a few feedback concerning the "Nullstellensatz".

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Example text

M = n 1a pas Be points f i x e s , e t d 6 f i n l t un momhisme ( 6 g d ir qnK)9 S stir une cousbe. 25 (lemme-cl6); cornme : ni? Z on a K . M = 0 I -Puisque le diviseur . (~K-& = Come h? = 0 ,le 0 systhe tmc . z=o IM ! 3 plVI ; si M~ 2 0 , donc rp (3) e s t une courbg! Remaroues 23 11 On peut m s l i o r e r notablement l'assertion c/ : s i S e s t une surface minimale, l e s y s t h e 1 nK 1 &t sans pbihts fixes ass que n $4 ; dbs que n 3 5 , l e morphisme T,K est un isomorphisme en dehors de certaines courbes rationnelles,.

B) = ( ~ * a . ~ * b=) ( ~ * a . e * ~=f (a x . y) d'o3 l e r d s u l t a t . 11 r e s t e 2 montrer que n f * e s t s u r j e c t i f . f i i s q u e 7i' e s t un revstement k t a l e de degr6 2, il e x i s t e une s u i t e s p e c t r e l e : 9 = I i P ( Z l ( 2 ) , H ~ ( A) )' ,gH*~(x' ) . cohomologie des groupes f i n i s donne : ,E = (-1 ) p 2 d P H ~ ( A)' -q9 ,~ e r ( u-E ) . / $oq+cp) pour p # 0 9 P Pour q s 2, l a r e s t r i c t i o n Iiq(A) -c H ~ ( A 'e) s t un isomorphisme; par s u i t e .

Soit w une 2-forme holomorphe non nulle sur 4. La forne &*w est inva- r i a n t e par a; e l l e e s t donc de l a forme ~ * 605 , a e s t une 2-forme m6romorphe sur X. x ce qui montre que h = 5 - d u A d t e s t holomorphe 2-forme holomorphe partout # 0 sur X, donc dt = A k a* (du A at), # 0 s u r Li. Ainsi o e s t une %3 0. S ' i l e x i s t a i t une 1-forme holomorphe non n u l l e sur X, on en dgduirait une 1-fome holomorphe 0 sur A invar'iante par 8, c e qui e s t impossible : donc q ( ~ =) 0 e t X e s t une surface K3 .

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Algebraic Surfaces by Arnaud Beauville (auth.), G. Tomassini (eds.)


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