Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1704.02543

Limit linear series for curves of compact type with three irreducible components

Gabriel Muñoz
View original source ↗Read source document ↗Export metadata ↓

Abstract

Our aim in this work is to study exact Osserman limit linear series on curves of compact type $X$ with three irreducible components. This case is quite different from the case of two irreducible components studied by Osserman. For instance, for curves of compact type with two irreducible components, every refined Eisenbud-Harris limit linear series has a unique exact extension. But, for the case of three irreducible components, this property is no longer true. We find a condition characterizing when a given refined Eisenbud-Harris limit linear series has a unique exact extension. To do this, it is necessary to understand how to construct exact extensions. We find a constructive method, which describes how to construct all exact extensions of refined limit linear series. By our method, we get that every refined limit linear series has at least one exact extension.

Explore related subjects

math.AG

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Gabriel Muñoz. 2017-07-12. Limit linear series for curves of compact type with three irreducible components. https://arxiv.org/abs/1704.02543

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↗