Résumé
Written to honour Miles Reid's 70th birthday, this volume contains contemporary research, both concrete and theoretical, spanning Reid's interests and career. Its definitive accounts of the state of the art in foundational areas will be of interest to graduate students and researchers in algebraic geometry, birational geometry and mirror symmetry.Written in celebration of Miles Reid's 70th birthday, this illuminating volume contains 11 papers by leading mathematicians in and around algebraic geometry, broadly related to the themes and interests of Reid's varied career. Just as in Reid's own scientific output, some of the papers give comprehensive accounts of the state of the art of foundational matters, while others give expositions of subject areas or techniques in concrete terms. Reid has been one of the major expositors of algebraic geometry and a great influence on many in this field - this book hopes to inspire a new generation of graduate students and researchers in his tradition.Happy Birthday Hamid Abban, Gavin Brown, Alexander Kasprzyk, Shigefumi Mori; 1. On stable cohomology of central extensions of elementary abelian groups Fedor Bogomolov, Christian Boehning, Alena Pirutka; 2. On projective 3-folds of general type with p_g = 2 Meng Chen, Yong Hu, Matteo Penegini; 3. 15-nodal quartic surfaces. Part I: quintic del Pezzo surfaces and congruences of lines in P^3 Igor V. Dolgachev; 4. Mori flips, cluster algebras and diptych varieties without unprojection Tom Ducat; 5. The mirror of the cubic surface Mark Gross, Paul Hacking, Sean Keel, Bernd Siebert; 6. Semi-orthogonal decomposition of a derived category of a 3-fold with an ordinary double point Yujiro Kawamata; 7. Duality and normalization, variations on a theme of Serre and Reid Janos Kollar, Hailong Dao; 8. Rationality of Q-Fano threefolds of large Fano index Yuri Prokhorov; 9. An exceptional locus in the perfect compacti cation of A_g Nicholas Shepherd-Barron, John Armstrong; 10. Variation of stable Birational types of Hypersurfaces Evgeny Shinder, Claire Voisin; 11. Triangle varieties and surface decomposition of hyper-Kahler manifolds Claire Voisin.Hamid Abban is Senior Lecturer in Mathematics at Loughborough University. His research mainly focuses on birational geometry of Fano varieties and various stability conditions on them. His work on birational geometry of 3-folds is influenced by the foundations laid by Reid. Gavin Brown is Professor of Mathematics at the University of Warwick. He has worked with Miles Reid for 30 years, as graduate student and collaborator on several joint papers. He worked in Sydney on the Magma Computational Algebra project, which led to the Graded Ring Database, an online resource which presents progress on Reid's graded ring approach to the classification of Fano 3-folds. Alexander Kasprzyk is Associate Professor in Geometry at the University of Nottingham. He applies combinatorial and computational techniques to classification problems in geometry. Whilst at Imperial College, he helped to establish a long-term research programme, strongly influenced by many of Reid's ideas, classifying Fano varieties using techniques from mirror symmetry. Shigefumi Mori is Director-General and Distinguished Professor at the Kyoto University Institute for Advanced Study (KUIAS), Kyoto University. Mori initiated the minimal model program jointly with Miles Reid during 1980-3, completed its 3-dimensional case in 1988, and received the Cole Prize and the Fields Medal in 1990. He served the International Mathematical Union as President during 2015-18.
