By Mauro C. Beltrametti, Fabrizio Catanese, Ciro Ciliberto
The papers during this quantity hide a large spectrum of algebraic geometry, from reasons idea to numerical algebraic geometry and are more often than not excited about better dimensional forms and minimum version application and surfaces of normal sort. part of the articles grew out of a convention in reminiscence of Paolo Francia held in Genova in September 2001 with nearly 70 individuals.
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Additional resources for Algebraic Geometry: A Volume in Memory of Paolo Francia ( De Gruyter Proceedings in Mathematics )
Serre, Geometrie algebrique et geometrie analytique, Ann. Inst. 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.
See [ 12],  and  for a full overview) we may expect the following picture for non-singular algebraic varieties over a field k (algebraically closed of characteristic zero for simplicity). Let X be a smooth proper k-scheme. , gr~m CHP(X)Q depends only on the Grothendieck motive h 2 P-i (X). 1. , CHP(X)aJg ~ ker(CHP(X) --+ NS P(X)). , CH P (X) ab is the intersection of all kernels of regular homomorphisms from CH P ( X)aJg to abelian varieties. Assume the existence of a universal regular homomorphism pP : CHP(X)aJg --+ A~;k(k) to (the group of k-points) of an abelian variety A~/k defined over the base L.
Jannsen, M. D. Lewis, J. Murre, A. Rosenschon, M. Saito, C. Soule and V. Voevodsky for discussions on some matters treated herein. Finally, I would like to thank Paolo Francia for his helpful insight and invaluable guidance in the vast field of algebraic geometry by dedicating this paper to his memory. Note that this research was carried out with smooth efficiency thanks to several foundations. I would like to thank the Tata Institute of Fundamental Research and the Institut Henri Poincare for their support and hospitality.