The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.

The volume consists of invited refereed research papers. The contributions cover a wide spectrum in algebraic geometry, from motives theory to numerical algebraic geometry and are mainly focused on higher dimensional varieties and Minimal Model Program and surfaces of general type.

A part of the articles grew out a Conference in memory of Paolo Francia (1951-2000) held in Genova in September 2001 with about 70 participants.

Lucian Badescu and Michael Schneider: Formal functions, connectivity and homogeneous spaces · Luca Barbieri-Viale: On algebraic 1-motives related to Hodge cycles · Arnaud Beauville: The Szpiro inequality for higher genus fibrations · Giuseppe Borrelli: On regular surfaces of general type with p_g = 2 and non-birational bicanonical map · Fabrizio Catanese and Frank-Olaf Schreyer: Canonical projections of irregular algebraic surfaces · Ciro Ciliberto and Margarida Mendes Lopes: On surfaces with p_g = 2, q = 1 and non-birational bicanonical map · Alberto Conte, Marina Marchisio and Jacob Murre: On unirationality of double covers of fixed degree and large dimension; a method of Ciliberto · Alessio Corti andMiles Reid:Weighted Grassmannians · Tommaso de Fernex and Lawrence Ein: Resolution of indeterminacy of pairs · Vladimir Guletskii and Claudio Pedrini: The Chow motive of the Godeaux surface · Yujiro Kawamata: Francia's flip and derived categories · Kazuhiro Konno: On the quadric hull of a canonical surface · Adrian Langer: A note on Bogomolov's instability and Higgs sheaves · Antonio Lanteri and Raquel Mallavibarrena: Jets of antimulticanonical bundles on Del Pezzo surfaces of degree ≤ 2 · Margarida Mendes Lopes and Rita Pardini: A survey on the bicanonical map of surfaces with p_g = 0 and K² ≥ 2 · Francesco Russo: The antibirational involutions of the plane and the classification of real del Pezzo surfaces · Vyacheslav.V. Shokurov: Letters of a birationalist IV. Geometry of log flips · Andrew J. Sommese, Jean Verschelde and Charles Wampler: A method for tracking singular paths with application to the numerical irreducible decomposition