In this paper we prove the Knop conjecture asserting that two smooth affine spherical varieties with the same weight monoid are equivariantly isomorphic. We also state and prove a uniqueness property for (not necessarily smooth) affine spherical varieties.
Dans cet article nous prouvons la conjecture de Knop qui affirme que deux variétés affines sphériques lisses avec le même monoïde des poids sont isomorphes de manière équivariante. On énonce et prouve également une propriété d’unicité pour des variétés affines sphériques non nécessairement lisses.
Keywords: Spherical varieties, weight monoids, systems of spherical roots, multiplicity free Hamiltonian actions
Mot clés : variété sphérique, monoïde
@article{AIF_2009__59_3_1105_0, author = {Losev, Ivan V.}, title = {Proof of the {Knop} conjecture}, journal = {Annales de l'Institut Fourier}, pages = {1105--1134}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {59}, number = {3}, year = {2009}, doi = {10.5802/aif.2459}, zbl = {1191.14075}, mrnumber = {2543664}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.2459/} }
TY - JOUR AU - Losev, Ivan V. TI - Proof of the Knop conjecture JO - Annales de l'Institut Fourier PY - 2009 SP - 1105 EP - 1134 VL - 59 IS - 3 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.2459/ DO - 10.5802/aif.2459 LA - en ID - AIF_2009__59_3_1105_0 ER -
Losev, Ivan V. Proof of the Knop conjecture. Annales de l'Institut Fourier, Volume 59 (2009) no. 3, pp. 1105-1134. doi : 10.5802/aif.2459. http://archive.numdam.org/articles/10.5802/aif.2459/
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