String cohomology of a toroidal singularity

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We construct explicitly regular sequences in the semigroup ring R = C[K] of lattice points of the graded cone K. We conjecture that the quotients of R by these sequences describe locally string-theoretic cohomology of a toroidal singularity associated to K. As a byproduct, we give an elementary proof of the result of Hochster that semigroup rings of rational polyhedral cones are Cohen-Macaulay.

Original languageEnglish (US)
Pages (from-to)289-300
Number of pages12
JournalJournal of Algebraic Geometry
Issue number2
StatePublished - Apr 2000
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Geometry and Topology


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