Search arXivSearch

arXiv · 2112.05960

On quadratically enriched excess and residual intersections

Abstract

We use recent duality results of Eisenbud--Ulrich to give tools to study quadratically enriched residual intersections when there is no excess bundle. We use this to prove a formula for the Witt-valued Euler number of an almost complete intersection. We give example computations of quadratically enriched excess and residual intersections.

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Tom Bachmann, Kirsten Wickelgren. 2023-07-04. On quadratically enriched excess and residual intersections. https://arxiv.org/abs/2112.05960

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