The Bauer Group of a Rational Surface.
The membership problem for polynomial ideals in terms of residue currents
We find a relation between the vanishing of a globally defined residue current on and solution of the membership problem with control of the polynomial degrees. Several classical results appear as special cases, such as Max Nöther’s theorem, for which we also obtain a generalization. Furthermore there are some connections to effective versions of the Nullstellensatz. We also provide explicit integral representations of the solutions.
The topological nature of algebraic contractions
Tie transformations of Dynkin graphs and singularities on quartic surfaces.