Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2405.15675

General type results for moduli of deformation generalised Kummer varieties

Matthew Dawes
View original source ↗Read source document ↗Export metadata ↓

Abstract

In arXiv:1710.01672, we obtained general type results for orthogonal modular varieties associated with moduli spaces of compact hyperkähler manifolds of deformation generalised Kummer type (also known as 'deformation generalised Kummer varieties'). The orthogonal modular varieties were defined in terms of an integer 2d, corresponding to the degree of polarisation of the associated hyperkähler manifolds. In arXiv:1710.01672, we showed these orthogonal modular varieties are of general type when 2d is square-free and sufficiently large. Here we show that the square-free condition can be removed.

Explore related subjects

math.AG

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Matthew Dawes. 2024-05-24. General type results for moduli of deformation generalised Kummer varieties. https://doi.org/10.1002/mana.70043

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↗