Edoardo Ballico, Fabrizio Catanese, Ciro Ciliberto's Classification of Irregular Varieties: Minimal Models and PDF

By Edoardo Ballico, Fabrizio Catanese, Ciro Ciliberto

ISBN-10: 0387552952

ISBN-13: 9780387552958

M. Andreatta,E.Ballico,J.Wisniewski: Projective manifolds containing huge linear subspaces; - F.Bardelli: Algebraic cohomology periods on a few specialthreefolds; - Ch.Birkenhake,H.Lange: Norm-endomorphisms of abelian subvarieties; - C.Ciliberto,G.van der Geer: at the jacobian of ahyperplane component of a floor; - C.Ciliberto,H.Harris,M.Teixidor i Bigas: at the endomorphisms of Jac (W1d(C)) whilst p=1 and C has basic moduli; - B. van Geemen: Projective types 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

Example text

Cl 14e eventually see that the picture of the limit of ~d(g,3 and that the two copies of Sd_i(g-Z,

Which are therefore divided into four groups, according to the four possibilities for the values of the vanishing sequences at R. Similarly each of the Pi's of the latter group is attached in one point to the copy of sdl(g-2,c~+2). These are therefore exceptional curves and can be contracted. Each of the Pi's of the second group is attached in one point to S~_2(g-2,c~-2) and to both copies of sl_l(g-2,~x) appearing in the limit. Similarly each of the Pl's of the third group is attached in $1 + I one point to d(g-2,

354. Then t h e r e is l- a scheme ~d(X)-~B over B whose points parametrize limit linear series of degree d and dimension r on the curve of ~r: X ~ B . Moreover ~ ( X ) - ~ B is flat over B if B is a smooth curve, the general fibre of it: X - ~ B is smooth and the special fibre is a curve of the type s h o w n in Fig. i. Proof. 3 in [EH1], w h e r e the existence of the scheme ~ ( X ) - ~ B is proved. Let B be a smooth curve and let q be a closed point of B such that the fibre Xq of it: X - , B is of compact type with n nodes.

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Classification of Irregular Varieties: Minimal Models and Abelian Varieties by Edoardo Ballico, Fabrizio Catanese, Ciro Ciliberto


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