Corpus ID: 207796375

Local Cohomology and Degree Complexes of Monomial Ideals.

  title={Local Cohomology and Degree Complexes of Monomial Ideals.},
  author={Jonathan L. O'Rourke},
  • Jonathan L. O'Rourke
  • Published 2019
  • Mathematics
  • This paper examines the dimension of the graded local cohomology $H_\mathfrak{m}^p(S/I)_\gamma$ for monomial ideals $I$. Due to a formula of Takayama, for $I \subset S$, the local cohomology of $S/I$ is related to the reduced homology of a simplicial complex, called the degree complex. We explicitly compute the degree complexes of ordinary and symbolic powers of sums and fiber products, as well as the degree complex of the mixed product, and then use homological techniques to discuss the… CONTINUE READING

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