Oberwolfach Reports
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Classical Algebraic Geometry
Organized by: David Eisenbud (1), Frank-Olaf Schreyer (2), Ravi Vakil (3) and Claire Voisin (4)
(1) Mathematical Sciences Research Institute, 1000 Centennial Drive, CA 94720-5070, BERKELEY, UNITED STATES(2) FB Mathematik und Informatik, Universität des Saarlandes, Postfach 15 11 50 - Geb. 27.1, D-66041, SAARBRÜCKEN, GERMANY
(3) Department of Mathematics, Stanford University, CA 94305-2125, STANFORD, UNITED STATES
(4) CNRS, Institut de Mathématiques de Jussieu, Case 247, 4 Place Jussieu, 75005, PARIS, FRANCE
Algebraic geometry studies properties of specific algebraic varieties, on the one hand, and moduli spaces of all varieties of fixed topological type on the other hand. Of special importance is the moduli space of curves, whose properties are subject of ongoing research. The rationality versus general type question of these and related spaces is of classical and also very modern interest with recent progress presented in the conference. Certain different birational models of the moduli space of curves and maps have an interpretation as moduli spaces of singular curves and maps. For specific varieties a wide range of questions was addressed, including extrinsic questions (syzygies, the k-secant lemma) and intrinsic ones (generalization of notions of positivity of line bundles, closure operations on ideals and sheaves).
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