On the volume of isolated singularities
On the volume of isolated singularities

Yuchen Zhang , University of Utah
Fine Hall 322
Boucksom, de Fernex and Favre defined a nonlogcanonical volume to study isolated singularities and developed several geometric results. Their definition is based on the intersection number of nef envelope of the log discrepancy bdivisor. In this talk, I will give an alternate definition of this volume by log canonical modification. I will study the lower bound of the volume in Gorenstein case using the new definition. Finally, I will give a threefold X with volume 0 but has no boundary \Delta such that the pair (X,\Delta) is log canonical.