By M. Andreatta, E. Ballico, J. Wiśniewski (auth.), Edoardo Ballico, Fabrizio Catanese, Ciro Ciliberto (eds.)
M. Andreatta,E.Ballico,J.Wisniewski: Projective manifolds containing huge linear subspaces; - F.Bardelli: Algebraic cohomology sessions on a few specialthreefolds; - Ch.Birkenhake,H.Lange: Norm-endomorphisms of abelian subvarieties; - C.Ciliberto,G.van der Geer: at the jacobian of ahyperplane portion of a floor; - C.Ciliberto,H.Harris,M.Teixidor i Bigas: at the endomorphisms of Jac (W1d(C)) while p=1 and C has basic moduli; - B. van Geemen: Projective versions of Picard modular kinds; - J.Kollar,Y.Miyaoka,S.Mori: Rational curves on Fano forms; - R. Salvati Manni: Modular types of the fourth measure; A. Vistoli: Equivariant Grothendieck teams and equivariant Chow teams; - Trento examples; Open difficulties
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Extra info for Classification of Irregular Varieties: Minimal Models and Abelian Varieties. Proceedings of a Conference held in Trento, Italy, 17–21 December, 1990
60 (i) In the firstdegeneration of ~g(g,g-2) shown in fig. 5 the curve ~ (g-l,g-1) is a ~i whereas we can apply induction to the curve ~i(g-l,g-5). Moreover ~=g-2. 6 the curve ~a(g-2,g) is a ~i and ja'=i. Hence ol ~ (g-2,g) can be contracted. Moreover ~_1(g-2,g-2) is a ~01, whereas we can apply induction to the curve ~_2(g-2,g-4), unless g=5, in which case this is again a pi. Moreover accordingly. ~=g-3. The third degeneration behaves 1 2 ) in the three pictures below: ~v'e show the three degenerations of ~g(g,g- s~_Ig-l,g-~) s~(g,g-i)--'~ I / g-2 copies f of ~I's \ Fig.
L, the moduli space of pointed curves of genus g. K~(C) can a priori be disconnected, its connected component of 0 being an abelian subvariety of Jac(W~(C)), the endomorphism ring of which contains Z: (*) Supported by CSCI 42 these are the trivial endomorphisms, c o m m o n to any complex torus, given by multiplication by integers. e. defined o v e r ~). Thi~ t h e o r e m is e x a c t l y w h a t is needed to e x t e n d to the case p=l, r = l t h e quoted r e s u l t a b o u t rationally d e t e r m i n e d line bundles.
4) C o r o l l a r y . There i~ a factorization C I --* C' C~ with f~ dtale and k e r f * = kerf2 and f*: J(C~) --* J injective. In terms of function fields the curve Ce corresponds to the maximal unramified extension of k(c')in k(C). 30 5. Prym varieties associated to a covering As in the last section let f: C ---* C' be a morphism of degree n > 2 of smooth projective curves of genus g and g' > 1. Recall the diagram (6) and denote by Z the abelian subvariety of J complementary to Y. By definition Z is called the Prym variety associated to the covering f, if the canonical polarization of J restricts to a multiple of a principal polarization on Z.
Classification of Irregular Varieties: Minimal Models and Abelian Varieties. Proceedings of a Conference held in Trento, Italy, 17–21 December, 1990 by M. Andreatta, E. Ballico, J. Wiśniewski (auth.), Edoardo Ballico, Fabrizio Catanese, Ciro Ciliberto (eds.)