Progress in algebraic geometry often comes through the introduction of new tools and ideas to tackle the classical problems the development of the field. Examples include new invariants that capture some aspect of geometry in a novel way, such as the derived category, and the extension of the class of geometric objects considered to allow constructions not previously possible, such as the transition from varieties to schemes or from schemes to stacks. Many famous old problems and outstanding conjectures have been resolved in this way over the last 50 years. While the new theories are sometimes studied for their own sake, they are in the end best understood in the context of the classical questions they illuminate. The goal of the workshop was to study new developments in algebraic geometry, with a view toward their application to the classical problems.
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Olivier Debarre, David Eisenbud, Frank-Olaf Schreyer, Ravi Vakil, Classical Algebraic Geometry. Oberwolfach Rep. 9 (2012), no. 2, pp. 1845–1893DOI 10.4171/OWR/2012/30