Non-Cohen–Macaulay projective monomial curves

Projective Monomial Curves in P

Bases and Ideal Generators for Projective Monomial Curves

In this article we study bases for projective monomial curves and the relationship between the basis and the set of generators for the defining ideal of the curve. We understand this relationship best for curves in P and for curves defined by an arithmetic progression. We are able to prove that the latter are set theoretic complete intersections.

Algebraic invariants of projective monomial curves associated to generalized arithmetic sequences

Multiplier Ideals of Monomial Space Curves

This paper presents a formula for the multiplier ideals of a monomial space curve. The formula is obtained from a careful choice of log resolution. We construct a toric blowup of affine space in such a way that a log resolution of the monomial curve may be constructed from this toric variety in a well controlled manner. The construction exploits a theorem of González Pérez and Teissier (2002).

Tropical secant graphs of monomial curves

T ROPICAL ALGEBRAIC GEOMETRY provides new tools to study elimination theory. Given a monomial curve t 7→ (1 : ti1 : . . . : tin) in Pn parameterized by a sequence of n coprime integers i1 < i2 < . . . < in, we wish to study its first secant variety. The goal of this project is to effectively calculate the TROPICALIZATION of the first secant variety of any monomial curve in Pn. Using methods fro...