Tropical secant graphs of monomial curves

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...

Tropical Curves and Metric Graphs

Tropical curves and metric graphs by Melody Tung Chan Doctor of Philosophy in Mathematics University of California, BERKELEY Professor Bernd Sturmfels, Chair In just ten years, tropical geometry has established itself as an important new field bridging algebraic geometry and combinatorics whose techniques have been used to attack problems in both fields. It also has important connections to are...

Geometry of curves with exceptional secant planes

We study curves with linear series that are exceptional with regard to their secant planes. Working in the framework of an extension of Brill-Noether theory to pairs of linear series, we prove that a general curve of genus g has no exceptional secant planes, in a very precise sense. We also address the problem of computing the number of linear series with exceptional secant planes in a one-para...

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).