Discrepancies on normal varieties
Friday, 1.6.12, 10:00-11:00, Raum 404, Eckerstr. 1
We will investigate the idea introduced by de Fernex and Hacon for studying singularities of normal varieties, via a pull-back for Weil divisors.\nWe will show some pathologies of the new definition and we will explain the main properties, with highlighting how the approach relates to properties of finite generation and to singularities in positive characteristic.
Klassifikation von Vektorbündeln
Friday, 15.6.12, 10:00-11:00, Raum 404, Eckerstr. 1
Separation coordinates and moduli spaces of stable curves
Friday, 29.6.12, 10:00-11:00, Raum 404, Eckerstr. 1
Separation coordinates are coordinates in which the classical Hamilton-Jacobi\nequation can be solved by a separation of variables. We establish a new and\npurely algebraic approach to the classification of separation coordinates\nunder isometries. This will be made explicit for the least non-trivial\nexample: the 3-sphere. In particular, we show that the moduli space of\nseparation coordinates on the 3-sphere is naturally isomorphic to a certain\nmoduli space of stable curves with marked points. Several generalisations of\nthis result will be proposed.