February 09, 2018
2:30 PM - 3:30 PM
Math Tower 5-127
|Ben Wu, Stony Brook University|
Pluricanonical forms and Gorenstein varieties
For a smooth variety, the canonical bundle is defined to be the line bundle which is the determinant of the cotangent bundle. A canonical divisor is a divisor whose associated line bundle is the canonical bundle. For normal varieties, we still have a notion of canonical divisor despite the presence of singularities. However, the sheaf associated to this canonical divisor may fail to be locally free, i.e. is not a line bundle. When the sheaf associated to some multiple of the canonical divisor on a normal variety is locally free, the variety is called Q-Gorenstein. In this talk, we will discuss how to define the canonical divisor on normal varieties and its associated sheaf and will discuss examples and non-examples of Q-Gorenstein varieties.