Socles of Buchsbaum modules , complexes and posets

  title={Socles of Buchsbaum modules , complexes and posets},
  author={Isabella Novik},
The socle of a graded Buchsbaum module is studied and is related to its local cohomology modules. This algebraic result is then applied to face enumeration of Buchsbaum simplicial complexes and posets. In particular, new necessary conditions on face numbers and Betti numbers of such complexes and posets are established. These conditions are used to settle in the affirmative Kühnel’s conjecture for the maximum value of the Euler characteristic of a 2k-dimensional simplicial manifold on n… CONTINUE READING
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