Dostert, Maria Vallentin, Frank
Published in
Advances in Geometry

We construct a new family of lattice packings for superballs in three dimensions (unit balls for the l3p $\begin{array}{} \displaystyle l^p_3 \end{array}$ norm) with p ∈ (1, 1.58]. We conjecture that the family also exists for p ∈ (1.58, log2 3 = 1.5849625…]. Like in the densest lattice packing of regular octahedra, each superball in our family of ...

Maican, Mario
Published in
Advances in Geometry

We study the moduli space of stable sheaves of Euler characteristic 1 supported on curves of arithmetic genus 3 contained in a smooth quadric surface. We show that this moduli space is rational. We compute its Betti numbers by studying the variation of the moduli spaces of α-semi-stable pairs. We classify the stable sheaves using locally free resol...

Brandt, Madeline Helminck, Paul Alexander
Published in
Advances in Geometry

We present an algorithm for computing the Berkovich skeleton of a superelliptic curve yn = f(x) over a valued field. After defining superelliptic weighted metric graphs, we show that each one is realizable by an algebraic superelliptic curve when n is prime. Lastly, we study the locus of superelliptic weighted metric graphs inside the moduli space ...

Lang, Julius
Published in
Advances in Geometry

It is proven by elementary methods that in dimension 2, every locally injective continuous map, sending the curves of a Ck-spray to curves of another Ck-spray as oriented point sets, is a Ck-diffeomorphism. This extends the result [1] for dimension three and higher from 1965.

Petronio, Carlo
Published in
Advances in Geometry

We continue our computation, using a combinatorial method based on Gronthendieck’s dessins d’enfant, of the number of (weak) equivalence classes of surface branched covers matching certain specific branch data. In this note we concentrate on data with the surface of genus g as source surface, the sphere as target surface, 3 branching points, degree...

Castañeda, Ángel Luis Muñoz
Published in
Advances in Geometry

We prove the existence of a linearization for singular principal G-bundles not depending on the base curve. This allow us to construct the relative compact moduli space of δ-(semi)stable singular principal G-bundles over families of reduced projective and connected nodal curves, and to reduce the construction of the universal moduli space over 𝓜g t...

Shanker, Gauree Kaur, Kirandeep
Published in
Advances in Geometry

We prove the existence of an invariant vector field on a homogeneous Finsler space with exponential metric, and we derive an explicit formula for the S-curvature of a homogeneous Finsler space with exponential metric. Using this formula, we obtain a formula for the mean Berwald curvature of such a homogeneous Finsler space.

Hirai, Hiroshi
Published in
Advances in Geometry

A simple lattice-theoretic characterization for affine buildings of type A is obtained. We introduce a class of modular lattices, called uniform modular lattices, and show that uniform modular lattices and affine buildings of type A constitute the same object. This is an affine counterpart of the well-known equivalence between projective geometries...

Brozos-Vázquez, M. García-Río, E. Gilkey, P. Valle-Regueiro, X.
Published in
Advances in Geometry

We examine the space of solutions to the affine quasi–Einstein equation in the context of homogeneous surfaces. As these spaces can be used to create gradient Yamabe solitons, conformally Einstein metrics, and warped product Einstein manifolds using the modified Riemannian extension, we provide very explicit descriptions of these solution spaces. W...

Denney, Tomme Hooker, Da’Shay Johnson, De’Janeke Robinson, Tianna Butler, Majid Claiborne, Sandernisha
Published in
Advances in Geometry

We describe the geometry of an arrangement of 24-cells inscribed in the 600-cell. In Section 7 we apply our results to the even unimodular lattice E8 and show how the 600-cell transforms E8/2E8, an 8-space over the field F2, into a 4-space over F4 whose points, lines and planes are labeled by the geometric objects of the 600-cell.