Algebraic Geometry--Open Problems by C. Ciliberto, F. Ghione, F. Orecchia

By C. Ciliberto, F. Ghione, F. Orecchia

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ROTH : Algebraic SARKISOV Mat. P. SERRE ET] : London Math. B. SEGRE : TYRELL Soc. Ergebnisse 34 ( 1 9 5 9 ) , Variazione Ann. Mat. : manifolds, : 57 ( 1 9 6 1 ) , Math. (1970). analysis, Appl. group The Enriques Math. 6, (1955). of of conic bundles, a unirational ed omotopia 50 (1960), On d e f o r m a t i o n s Math. der York variety~ 481-484. continua Pura 897-898. Press to 177-202. fundamental Soc. University Contributions automorphisms 17 ( 1 9 8 1 ) , K. TIMMERSCHEIDT J. Oxford I. threefolds, On t h e J.

Moreover sheaf on U T d e f i n e d = dimHO(~-l(t) ,Lt) Moreover flat m o r p h i s m . Therefore rank = h 0 (t,i) (f,i®k(t)) (t,i(t)). @ s,A I(T) . Let on T. = isomorphism Proof. is c o n s t a n t by s(t) in p r o j e c t i v e = ~ * A 2(T) hO(t,i) diagram we study the g r o u p A2(U) . The p r o j e c t i o n a natural 2 and V s:T ÷ U T is the s e c t i o n To b e g i n with, of d e g r e e U > T base finite = d i m H O ~ I, ]pl(1)) i is flat on T since f,i is a locally (see [HI, by the free p.

Les Si H est rationnel de p 5 ~ la question X admettant un groupe vectoriel irrationnelle. 4. de Z a r i s k i dans 4 est u n de c u b i q u e s , la de X × ~ I ) souvent ? de F a n o " s ' a p p r o c h e en e s t assertions ~n~ri~ue irrationnelle l'espace de d i m e n - : rationnelle, ou G e s t rement I1 doubles de c o d i m e n s i o n tordue" On r e n c o n t r e de de rationnelle des vari~t~s ~videmment unirationnelle. au § 9 u n e v a r i ~ t ~ le int~ressant irrationnelle vari~t~ cro~t.

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