Liftings of a monomial curve
Commutative Algebra
2018-10-03 v2 Algebraic Geometry
Abstract
We study an operation, that we call lifting, creating non-isomorphic 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 nothing but the Betti sequence of the original curve.
Cite
@article{arxiv.1803.07285,
title = {Liftings of a monomial curve},
author = {Mesut Şahin},
journal= {arXiv preprint arXiv:1803.07285},
year = {2018}
}