Geometry of Moduli

The proceedings from the Abel Symposium on Geometry of Moduli, held at Svinøya Rorbuer, Svolvær in Lofoten, in August 2017, present both survey and research articles on the recent surge of developmentsin understanding moduli problems in algebraic geometry. Written bymany of the main contributors to this evolving subject, the book provides a comprehensivecollection of new methods and the various directions in which moduli theory isadvancing. These include the geometry of moduli spaces, non-reductive geometric invarianttheory, birational geometry, enumerative geometry, hyper-kähler geometry, syzygies ofcurves and Brill-Noether theory and stability conditions. Moduli theory is ubiquitous inalgebraic geometry, and this is reflected in the list of moduli spaces addressed in this volume: sheaveson varieties, symmetric tensors, abelian differentials, (log) Calabi-Yau varieties, points onschemes, rational varieties, curves, abelian varieties and hyper-Kähler manifolds.