Some Basic Results on Actions of Nonaffine Algebraic Groups -- On Chevalley–Shephard–Todd’s Theorem in Positive Characteristic -- Families of Affine Fibrations -- On the Depth of Modular Invariant Rings for the Groups × -- Kählerian Reduction in Steps -- On Orbit Decompositions for Symmetric -Varieties -- Root Systems for Levi Factors and Borel–de Siebenthal Theory -- Polarizations and Nullcone of Representations of Reductive Groups -- Decomposing Symmetric Powers of Certain Modular Representations of Cyclic Groups -- Differential Operators on Grassmann Varieties.

A group of Gerry Schwarz’s colleagues and collaborators gathered at the Fields Institute in Toronto for a mathematical festschrift in honor of his 60th birthday. This volume is an outgrowth of that event, covering the wide range of mathematics to which Gerry Schwarz has either made fundamental contributions or stimulated others to pursue. The articles are a sampling of modern day algebraic geometry with associated group actions from its leading experts, with a particular focus on characteristic 0 and modular invariant theory. Contributors: M. Brion A. Broer D. Daigle J. Elmer P. Fleischmann G. Freudenberg D. Greb P. Heinzner A. Helminck B. Kostant H. Kraft R. J. Shank W. Traves N. R. Wallach D. Wehlau