On pseudo symmetric monomial curves

Noncommutative Monomial Symmetric Functions

This presentation will introduce noncommutative analogs of monomial symmetric functions (and their dual, forgotten symmetric functions). In analogy to the classical theory, expansion of ribbon Schur functions in this basis in nonnegative. Moreover, one can define fundamental noncommutative symmetric functions by analogy with quasi-symmetric theory. The expansion of ribbon Schur functions in thi...

Projective Monomial Curves in P

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...

Hilbert Functions of Gorenstein Monomial Curves

It is a conjecture due to M. E. Rossi that the Hilbert function of a one-dimensional Gorenstein local ring is non-decreasing. In this article, we show that the Hilbert function is non-decreasing for local Gorenstein rings with embedding dimension four associated to monomial curves, under some arithmetic assumptions on the generators of their defining ideals in the noncomplete intersection case....