Geometry Seminar - Abstracts


10 February 2016, 16:00 - 17:00, in HG00.310
Gert Heckmann (Radboud Universiteit)
Hyperbolic Coxeter groups and quartic curves


The Weyl group of type E7 has a presentation as factor group of the Coxeter group on the tetrahedral diagram T10 (by definition the simply laced Coxeter diagram with for its 10=(4+6) nodes the 4 vertices and the 6 midpoints of the edges of a tetrahedron and as simple bonds the 12 half edges) modulo deflation of the free octagons. We shall explain this presentation in geometric terms (through the moduli space of maximal real smooth quartic curves). This is joint work with Sander Rieken, and generalizes a previously obtained similar presentation for the Weyl group of type E6 in connection with maximal real (that is 27 real lines) smooth cubic surfaces.

We shall give a pedestrian review of Coxeter group theory and subsequently explain the desired presentation using results of the thesis by Sander Rieken (also to be explained a little).