402 research outputs found
Rational plane curves parameterizable by conics
We introduce the class of rational plane curves parameterizable by conics as
an extension of the family of curves parameterizable by lines (also known as
monoid curves). We show that they are the image of monoid curves via suitable
quadratic transformations in projective plane. We also describe all the
possible proper parameterizations of them, and a set of minimal generators of
the Rees Algebra associated to these parameterizations, extending well-known
results for curves parameterizable by lines.Comment: 28 pages, 1 figure. Revised version. Accepted for publication in
Journal of Algebr
Apery and micro-invariants of a one dimensional Cohen-Macaulay local ring and invariants of its tangent cone
Given a one-dimensional Cohen-Macaulay local ring we compare several sets of
invariants (micro-invariants, Apery invariants and invariants of the tangent
cone) and give explicit formulas relating them. We show that, in fact, they
coincide if and only if the tangent cone of the ring is Cohen-Macaulay. Some
explicit computations are also given, particularly in the case of semigroup
rings.Comment: 20 page
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