Algebraic Threefolds: Proceedings of the 2nd1981 Session of by Kenji Ueno (auth.), Alberto Conte (eds.)

By Kenji Ueno (auth.), Alberto Conte (eds.)

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Extra resources for Algebraic Threefolds: Proceedings of the 2nd1981 Session of the Centro Internazionale Matematico Estivo (C.I.M.E.), Held at Varenna, Italy, June 15–23, 1981

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Is bimeromorphically 31 equivalent to an analytic is an elliptic c) If ~ is a surface with A(M) whose connected Remark curve of genus k(M) I) If = O, Example g~ 2. fibre Mx Example are K 3 are complex equivalent of ~ tori but ~ to an analytic is bimeromorphically K 3 threefold threefold Such threefold M fibres fibre bundle threefold belonging is not over A(M). which belongs t(M). to the class of the Albanese mapping is obtained by the threefold invnlution in of each ~ ~t : Mt---~ C, e U' and resolving its singularities.

When no c o n f u s i o n +C2) - 2 ~ v . D V . (here we use the fact that we have V by a p p l y i n g , 0 -< i -< n . (-| In the f o l l o w i n g instead on is the second e) K o d a i r a are o b t a i n e d Let = hn-i(~7-D)_ b) R i e m a n n - R o c h we have OF FANO T H R E E F O L D S the irregularity q(V) = hl(OV ) = 0 . K 41 COROLLARY 4. Pic(V) ~ H2(V,Zg) . PROOF. Look to the exponential sequence 0 --§ ~ --+ exp r) --+ O* --+ h I (0 V) = h 2 (0 V) = 0 . and use COROLLARY Kv. C2(V) 5. = -24 i PROOF.

Hitchin, N. , and I. M. , Self-duality in four-dimensional Riemannisn geometry. Proc. Royal Soc. London A 362 (1978), 425-461. , Sur les varietes analytiques comples. Ann. Sci. Ecole Norm. Sup. 73 (1956), 157-202. , Application de l'espace des cycles a la classification bimeromorphm des espaces analytiques Kahleriens compacts, preprint 1980. , On the structure of compact complex manifolds in C, to appear. 6 Fujita, T. On K~hler fibre spaces over curves, J. Math. Soc. Japan, 3_~0 11978), 779-794.

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