Threefold flops via matrix factorization

Carina Curto, David R. Morrison

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


The explicit McKay correspondence, as formulated by Gonzalez- Sprinberg and Verdier, associates to each exceptional divisor in the minimal resolution of a rational double point, a matrix factorization of the equation of the rational double point. We study deformations of these matrix factorizations, and show that they exist over an appropriate "partially resolved" deformation space for rational double points of types A and D. As a consequence, all simple flops of lengths 1 and 2 can be described in terms of blowups defined from matrix factorizations. We also formulate conjectures which would extend these results to rational double points of type E and simple flops of length greater than 2.

Original languageEnglish (US)
Pages (from-to)599-627
Number of pages29
JournalJournal of Algebraic Geometry
Issue number4
StatePublished - 2013

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Geometry and Topology


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