caa a22 4500 445862246 CHVBK 20180317145447.0 cr unu---uuuuu 170323e20110301xx s 000 0 eng 10.1007/s00031-010-9108-3 doi (NATIONALLICENCE)springer-10.1007/s00031-010-9108-3 Le Barbier Grünewald Michaël Max-Planck-Institut für Mathematik, Vivatsgasse 7, 53 111, Bonn, Germany aut The variety of reductions for a reductive symmetric pair [Elektronische Daten] [Michaël Le Barbier Grünewald] We define and study the variety of reductions for a complex reductive symmetric pair (G, θ), which is the natural compactification of the set of its Cartan subspaces. These varieties generalize the varieties of reductions for the Severi varieties studied by Iliev and Manivel, which are Fano varieties. We develop a theoretical basis to the study of these varieties of reductions, and relate their geometry to some problems in representation theory. A very useful result is the rigidity of semisimple elements in deformations of algebraic subalgebras of Lie algebras. We use it to show that the closure of a decomposition class is a union of decomposition classes. We apply this theory to the study of other varieties of reductions in a companion paper, which yields two new Fano varieties. Springer Science+Business Media, LLC, 2010 Transformation Groups SP Birkhäuser Verlag Boston 16/1(2011-03-01), 1-26 1083-4362 16:1<1 2011 16 31 https://doi.org/10.1007/s00031-010-9108-3 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00031-010-9108-3 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Le Barbier Grünewald Michaël Max-Planck-Institut für Mathematik, Vivatsgasse 7, 53 111, Bonn, Germany aut NATIONALLICENCE 773 0- Transformation Groups SP Birkhäuser Verlag Boston 16/1(2011-03-01), 1-26 1083-4362 16:1<1 2011 16 31 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer