LIFTINGS OF A MONOMIAL CURVE


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ŞAHİN M.

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, vol.98, no.2, pp.230-238, 2018 (SCI-Expanded) identifier identifier

Abstract

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.