Differential operators on monomial curves

Differential operators on monomial rings

Rings of differential operators are notoriously difficult to compute. This paper computes the ring of differential operators on a Stanley-Reisner ring R. The D-module structure of R is determined. This yields a new proof that Nakai’s conjecture holds for Stanley-Reisner rings. An application to tight closure is described. @ 1999 Elsevier Science B.V. All rights reserved. AMS Clas.@cation: Prima...

Mad Subalgebras of Rings of Differential Operators on Curves

We study the maximal abelian ad-nilpotent (mad) subalgebras of the domains D Morita equivalent to the first Weyl algebra. We give a complete description both of the individual mad subalgebras and of the space of all such. A surprising consequence is that this last space is independent of D . Our results generalize some classic theorems of Dixmier about the Weyl algebra.

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...