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Birational Invariants and Differential Forms (part 2, talk 1)

Talker: Wolfgang Stöcher  

In part 2, we defined the adjoint ideals in terms of differential forms. The main topic of part 3 is to prove that these adjoint ideals can be computed exactly in the same way as in the well-known curve case, by forcing certain orders at the singularities. To do this, we have to introduce some sheaf theory: direct image functor, inverse image functor, invertible sheaves, projection formula. Moreover, it is necessary to give an explicit formula for the "dualizing sheaf" of rational differential forms. Using these tools, we perform most of the calculations very explicitly, in order to show how these objects are computationally handled.