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

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

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 ok² =1,2, q=pg=0.- F. Catanese: On a category of surfaces of common type.- I. Dolgacev: Algebraic surfaces with p=pg =0.- A. Tognoli: a few comments in regards to the "Nullstellensatz".

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Extra resources for Algebraic Surfaces

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Rapelons (Thbor8me 18,lbre partie) qu'une surface K3 est une sur'face vbrifiant'K I ,0, q = 0. Les intersections comple'tes V4, V2,3, V2 sont des 0 surfaces K 3 (cf. exemple 16, 18re partie); 0 plus gdndrakment, pour tout g r 3 il existe une lfamiile de surfaces K3 de degrb 2g-2 dans pg. Nous allons indiquer cons%hction particuli8re de surfaces K3, '8 partir de surfaces abb- ~e . liennes Soit h une surface abslienne. ,a16, qui sont les points d'grdre 2 de A. 118clatementde ces 16 $oints, Ei le diviseur exceptionnel i s 16).

F ' ) l a fibre 2 q6nCrique d'une f i b r a t i o n de ~ummer. mant c y c l e s e f f e c t i f s en c y c l e s e f f e c t i f s , e t t e l que'f'(f) X g X' = f'. sont i s o m o r ~ h e s . trans- Ddmonstration': Compte t e n u d e l a p r o p o s i t i o n 7, il s u f f i t d e prouver que q(%) = LX, . C Li 1 & a m ~ i c ( ~ ) , ' d ' o i if' = 2 % ~) + z % L ~ ) r dans p i c ( X q ) . Comme l e s s e u l e s dEcompositions d e f ' en s o m e de d i v i s e u r s e f f e c t i f s s o n t de .

Engendr6 par l e s composantes des f i b r e s d e q . ej = 0 2 nun? du produit pour 1 < i < 3 poui o -< i s 3 pour 1 S i S j s c a l a i r e d g f i n i par: ,' S 3 . I1 r g s u l t e a u s s i t d t de l a proposition 8 que lorsque f e s t l a f i b r e d'une fi: 4 bration de Kummer, s X ( f ) e s t isomorphe come module quadratique b (DL) . Proposition 10. if i b r e s con- =, f l a c l a s s e dans P ~ C ( Xd'une ) f i b r e de q. ; a l o r s , X est: une surface de Kummer sp'eciale,, & q e s t une f i b r a t i o n de Kummer.

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