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Abstract des Vortrages von Matthias Zach

Computation of Vanishing Cycles via blowup of Syzygies

I will report on the Tjurina Modification in family. It can be seen as a special way of blowing up an isolated singularity and was initially applied by Tjurina to study rational triple point singularities. We generalized the technique to isolated non-complete intersection singularities and used it to compute the vanishing topology of simple Cohen-Macaulay codimension 2 threefold singularities. Here the appearance of cycles in lower degrees shows a nice interplay with the Tjurina modification applied to the total space of a deformation.