## 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.