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2 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
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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.

  • LIFTINGS OF A MONOMIAL CURVE

  • Part of
  • MESUT ŞAHİN
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 98 / Issue 2 / October 2018
    Published online by Cambridge University Press:
    05 July 2018, pp. 230-238
    Print publication:
    October 2018
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  • We study an operation, that we call lifting, creating nonisomorphic monomial curves from a single monomial curve. Our main result says that all but finitely many liftings of a monomial curve have Cohen–Macaulay tangent cones even if the tangent cone of the original curve is not Cohen–Macaulay. This implies that the Betti sequence of the tangent cone is eventually constant under this operation. Moreover, all liftings have Cohen–Macaulay tangent cones when the original monomial curve has a Cohen–Macaulay tangent cone. In this case, all the Betti sequences are just the Betti sequence of the original curve.