By Mauro C. Beltrametti, Fabrizio Catanese, Ciro Ciliberto

The papers during this quantity hide a large spectrum of algebraic geometry, from explanations idea to numerical algebraic geometry and are regularly serious about better dimensional kinds and minimum version application and surfaces of basic sort. part of the articles grew out of a convention in reminiscence of Paolo Francia held in Genova in September 2001 with nearly 70 contributors.

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Fourier 6 (1955), 1-42. [Se] F. Severi, Alcune proprieta fondamentali dell'insieme dei punti singolari di una funzione analitica di piu variabili, Mem. Accad. Ital. 3 ( 1932). [So] A. J. Sommese, Submanifolds of abelian varieties, Math. Ann. 233 ( 1978), 229-256. [Sp] R. Speiser, Cohomological dimension and abelian varieties, Amer. J. Math. 95 (1973), 1-34. [Z] 0. Zariski, Theory and applications of holomorphic functions on algebraic varieties over arbitrary ground fields. Mem. Amer. Math. Soc.

Lubke, Beweis einer Vermutung von Hartshorne fUr den Fall homogener Mannigfaltigkeiten, J. Reine Angew. Math. 316 ( 1980), 215-220. [M] D. Mumford, Abelian Varieties, Tata Inst. Fund. Res. Lect. Math. Bombay 1968. [R] Z. Ran, On subvarieties of abelian varieties, Invent. Math. 62 ( 1981 ), 45H79. [Ro] H. Rossi, Continuation of subvarieties of projective varieties, A mer. J. Math. 91 ( 1969), 565-575. [RVdV] R. Remmert and A. Van de Ven, Zur Funktionentheorie homogener komplexer Mannigfaltigkeiten, Topology 2 (1963), 137-157.

IQ). I. The following square commutes, yielding a motivic "cycle class map". 2. The image of the motivic "cycle class map" is the Hodge 1-motive of the Q-Hodge structure H 2P+i (X). 3. We have that THodge(S;·P) ;;;:: H2p+i (X)h. 5. Note that if X is smooth and proper then H 2P+i (X) is pure and H 2P+i (X) 11 ~ 0 if and only if i = 0, -I (p fixed). In this case, the above conjecture follows from the reformulation of Grothendieck-Hodge conjecture for H 2 P(X) and H2p-1(X). 3. Local Hodge theory See [II] for notations, definitions and properties of mixed Hodge structures.