Download PDF by Mauro C. Beltrametti, Fabrizio Catanese, Ciro Ciliberto: Algebraic Geometry: A Volume in Memory of Paolo Francia ( De
By Mauro C. Beltrametti, Fabrizio Catanese, Ciro Ciliberto
The papers during this quantity hide a large spectrum of algebraic geometry, from reasons conception to numerical algebraic geometry and are generally fascinated with larger dimensional forms and minimum version software and surfaces of normal kind. part of the articles grew out of a convention in reminiscence of Paolo Francia held in Genova in September 2001 with nearly 70 members.
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Additional resources for Algebraic Geometry: A Volume in Memory of Paolo Francia ( De Gruyter Proceedings in Mathematics )
Thus the presheaf of mixed Hodge structures (9) can be sheafified to a Zariski Qt-mixed sheaf. 4]). 1. Denote Jl~(Qt(t)) the Qt-mixed sheaf obtained hereabove. For X. a simplicial C-scheme denote Je~ • the simplicial Qt-mixed sheaf given by Je~p on the component X P. If X has algebraic dimension n then all its Zariski open affines U do have dimension ::5 n, thus Je~ = 0 for r > n. 2. The Zariski cohomology groups H * (X, Je~) carry oo-mixed Hodge structures. Possibly non-zero Hodge numbers of H*(X, Jl~) are in the finite set [0, r] x [0, r].
4. Edge maps Recall that the classical cycle class maps can be obtained via edge homomorphisms in the coniveau spectral sequence. This is a consequences of Bloch's formula [8). Working simplicially we then construct certain cycle class maps for singular varieties via edge maps in the local-to-global spectral sequence. We first show that the results of  hold in the category of oo-mixed Hodge structures. 1. 8] the cohomology groups H~(X) (= H*(XmodXZ, Z) in Deligne's notation) carry a mixed Hodge structure fitting into long exact sequences .
Gillet, M. Hanamura, U. 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.