12 research outputs found
Local Euler obstructions of toric varieties
We use Matsui and Takeuchi's formula for toric A-discriminants to give
algorithms for computing local Euler obstructions and dual degrees of toric
surfaces and 3-folds. In particular, we consider weighted projective spaces. As
an application we give counterexamples to a conjecture by Matsui and Takeuchi.
As another application we recover the well-known fact that the only defective
normal toric surfaces are cones
Polar degrees and closest points in codimension two
Suppose that is a toric variety of codimension
two defined by an integer matrix , and let be a Gale
dual of . In this paper we compute the Euclidean distance degree and polar
degrees of (along with other associated invariants) combinatorially
working from the matrix . Our approach allows for the consideration of
examples that would be impractical using algebraic or geometric methods. It
also yields considerably simpler computational formulas for these invariants,
allowing much larger examples to be computed much more quickly than the
analogous combinatorial methods using the matrix in the codimension two
case.Comment: 25 pages, 1 figur
Chow groups and pseudoffective cones of complexity-one T-varieties
Abstract We show that the pseudoeffective cone of k -cycles on a complete complexity-one T -variety is rational polyhedral for any k , generated by classes of T -invariant subvarieties. When X is also rational, we give a presentation of the Chow groups of X in terms of generators and relations, coming from the combinatorial data defining X as a T -variety