Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 0709.4403

Minimal Affine Coordinates for SL(3,C) Character Varieties of Free Groups

Sean Lawton
View original source ↗Read source document ↗Export metadata ↓

Abstract

Let X be the moduli of SL(3,C) representations of a rank r free group. In this paper we determine minimal generators of the coordinate ring of X. This at once gives explicit global coordinates for the moduli and determines the dimension of the moduli's minimal affine embedding. Along the way, we utilize results concerning the moduli of r-tuples of matrices in gl(3,C). Consequently, we also state general invariant theoretic correspondences between the coordinate rings of the moduli of r-tuples of elements in gl(n,C), sl(n,C), and SL(n,C).

Explore related subjects

math.AGmath.AC

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Sean Lawton. 2008-07-03. Minimal Affine Coordinates for SL(3,C) Character Varieties of Free Groups. https://doi.org/10.1016/j.jalgebra.2008.06.031

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

G3-Criteria and Applications

The G3-property of a subvariety was introduced by Hironaka-Matsumura, and plays an important role for deducing connectedness and extension results. Unfortunately, it's a rather elusive notion, which is not always easy to establish. Most of the existing work is concentrated on subvarieties of homogeneous varieties. The first goal of this article is to show that mobility assumptions on the subvariety, considered in works of Badescu, Chow, Debarre, Voisin, yield a certain partial positivity property, slightly stronger than G3, previously introduced by the author. Second, we apply the result to prove that, in numerous situations, the splitting of the normal bundle of a smooth two-codimensional subvariety implies that it is a complete intersection.

math.AG↗
arXiv2026

Nodal degeneration of chiral algebras I: Global structure and gluing formula

We define a natural extension of a universal factorization algebra $\mathcal{A}$ to families of stable punctured curves, by integrating over all semistable modifications. We prove that the resulting sheaf of factorization homology satisfies a natural gluing formula, by tensoring over a certain derived associative algebra $\mathfrak{Z}_{\mathcal{A}}^0$, generalizing the Verlinde formula for gluing of conformal blocks.

math.AG↗