Divisorial models on non-Q-Gorenstein varieties
Stefano Urbinati, University of Utah

Based on the construction of de Fernex and Hacon, we study the behavior of the singularities on non-Q-Gorenstein varieties, in particular for which the canonical ring is not a finitely generated O_X-algebra. We give an example of a non Q-Gorenstein variety whose canonical divisor has an irrational valuation and example of a non Q-Gorenstein variety which is canonical but not klt. We also give an example of an irrational jumping number and we prove that there are no accumulation points for the jumping numbers of normal non-Q-Gorenstein varieties with isolated singularities. We also prove that Canonical singularities are equivalent to the finite generation of the canonical ring.