On the computation of a-invariants

Abstract

Thea-invariant of a graded Cohen-Macaulay ring is the least degree of a generator of its graded canonical module. We compute thea-invariants of (i) graded algebras with straightening laws on upper semi-modular lattices and (ii) the Stanley-Reisner rings of shellable weighted simplicial complexes. The formulas obtained are applied to rings defined by determinantal and pfaffian ideals.

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Bruns, W., Herzog, J. On the computation of a-invariants. Manuscripta Math 77, 201–213 (1992). https://doi.org/10.1007/BF02567054

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Keywords

  • Partial Order
  • Simplicial Complex
  • Minimal Element
  • Hilbert Series
  • Canonical Module