• Corpus ID: 18194085

Gorenstein Threefold Singularities with Small Resolutions via Invariant Theory for Weyl Groups

  title={Gorenstein Threefold Singularities with Small Resolutions via Invariant Theory for Weyl Groups},
  author={Sheldon Katz and David R. Morrison},
  journal={arXiv: Algebraic Geometry},
We classify simple flops on smooth threefolds, or equivalently, Gorenstein threefold singularities with irreducible small resolution. There are only six families of such singularities, distinguished by Koll{a}r's {\em length} invariant. The method is to apply invariant theory to Pinkham's construction of small resolutions. As a by-product, generators of the ring of invariants are given for the standard action of the Weyl group of each of the irreducible root systems. 

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