Gavril Farkas – författare

This book provides an overview of the latest progress on rationality questions in algebraic geometry. It discusses new developments such as universal triviality of the Chow group of zero cycles, various aspects of stable birationality, cubic and Fano fourfolds, rationality of moduli spaces and birational invariants of group actions on varieties, contributed by the foremost experts in their fields.

The question of whether an algebraic variety can be parametrized by rational functions of as many variables as its dimension has a long history and played an important role in the history of algebraic geometry. Recent developments in algebraic geometry have made this question again a focal point of research and formed the impetus to organize a conference in the series of conferences on the island of Schiermonnikoog. The book follows in the tradition of earlier volumes, which originated from conferences on the islands Texel and Schiermonnikoog.

This bookprovides an overview of the latest developments concerning the moduli of K3surfaces. It is aimed at algebraic geometers, but is also of interest to numbertheorists and theoretical physicists, and continues the tradition of relatedvolumes like “The Moduli Space of Curves” and “Moduli of Abelian Varieties,”which originated from conferences on the islands Texel and Schiermonnikoog andwhich have become classics.

K3 surfacesand their moduli form a central topic in algebraic geometry and arithmeticgeometry, and have recently attracted a lot of attention from bothmathematicians and theoretical physicists. Advances in this field often resultfrom mixing sophisticated techniques from algebraic geometry, lattice theory,number theory, and dynamical systems. The topic has received significantimpetus due to recent breakthroughs on the Tate conjecture, the study ofstability conditions and derived categories, and links with mirror symmetry andstring theory. At the sametime, the theory of irreducible holomorphicsymplectic varieties, the higher dimensional analogues of K3 surfaces, hasbecome a mainstream topic in algebraic geometry.

Contributors:S. Boissière, A. Cattaneo, I. Dolgachev, V. Gritsenko, B. Hassett, G. Heckman,K. Hulek, S. Katz, A. Klemm, S. Kondo, C. Liedtke, D. Matsushita, M.Nieper-Wisskirchen, G. Oberdieck, K. Oguiso, R. Pandharipande, S. Rieken, A. Sarti, I.Shimada, R. P. Thomas, Y. Tschinkel, A. Verra, C. Voisin.