The geometry of commuting varieties of reductive groups
Carlos Florentino (Faculty of Sciences - University of Lisbon)
Abstract: Let $R_r(G)$ be the (connected component of the identity of the) variety of commuting $r$-tuples of elements of a complex reductive group $G$. We determine the mixed Hodge structure on the cohomology of the representation variety $R_r(G)$ and of the character variety $R_r(G)/G$, for general $r$ and $G$. We also obtain explicit formulae (both closed and recursive) for the mixed Hodge polynomials, Poincaré polynomials and Euler characteristics of these representation and character varieties. In the character variety case, this gives the counting polynomial over finite fields, and some results also apply to character varieties of nilpotent groups.
This is joint work with S. Lawton and J. Silva (arXiv:2110.07060).
algebraic geometrydifferential geometrysymplectic geometry
Audience: researchers in the topic
Series comments: To receive the series announcements, which include the
Zoom access password*, please register in
math.tecnico.ulisboa.pt/seminars/geolis/index.php?action=subscribe#subscribe
*the last announcement for a seminar is sent 2 hours before the seminar.
Geometria em Lisboa video channel: educast.fccn.pt/vod/channels/bu46oyq74
Organizers: | Jose Mourao*, Rosa Sena Dias, SÃlvia Anjos* |
*contact for this listing |