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3 results

  • BETTI NUMBERS FOR CERTAIN COHEN–MACAULAY TANGENT CONES

  • Part of
  • MESUT ŞAHİN, NİL ŞAHİN
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 99 / Issue 1 / February 2019
    Published online by Cambridge University Press:
    30 August 2018, pp. 68-77
    Print publication:
    February 2019
    • Article
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  • We compute Betti numbers for a Cohen–Macaulay tangent cone of a monomial curve in the affine $4$-space corresponding to a pseudo-symmetric numerical semigroup. As a byproduct, we also show that for these semigroups, being of homogeneous type and homogeneous are equivalent properties.

  • Filtering free resolutions

  • Part of
  • David Eisenbud, Daniel Erman, Frank-Olaf Schreyer
  • Journal:
    Compositio Mathematica / Volume 149 / Issue 5 / May 2013
    Published online by Cambridge University Press:
    18 March 2013, pp. 754-772
    Print publication:
    May 2013
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  • A recent result of Eisenbud–Schreyer and Boij–Söderberg proves that the Betti diagram of any graded module decomposes as a positive rational linear combination of pure diagrams. When does this numerical decomposition correspond to an actual filtration of the minimal free resolution? Our main result gives a sufficient condition for this to happen. We apply it to show the non-existence of free resolutions with some plausible-looking Betti diagrams and to study the semigroup of quiver representations of the simplest ‘wild’ quiver.