Search arXivSearch

arXiv · math/0404078

Moduli of roots of line bundles on curves

Abstract

We treat the problem of completing the moduli space for roots of line bundles on curves. Special attention is devoted to higher spin curves within the universal Picard scheme. Two new different constructions, both using line bundles on nodal curves as boundary points, are carried out and compared with pre-existing ones.

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Lucia Caporaso, Cinzia Casagrande, Maurizio Cornalba. 2007-02-21. Moduli of roots of line bundles on curves. https://arxiv.org/abs/math/0404078

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

KEEP EXPLORING

Related papers

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

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