Bilgin, Merve Ersoy, Soley
Published in
Advances in Applied Clifford Algebras

In this paper, we study the four-dimensional real algebra of bihyperbolic numbers. Under consideration of the spectral representation of the bihyperbolic numbers, we give a partial order of bihyperbolic numbers which allows us to obtain some relations in the ordered vector space of bihyperbolic numbers. Moreover, we state that the set of bihyperbol...

Carocca, Angel Lange, Herbert Rodríguez, Rubí E.
Published in
Archiv der Mathematik

An automorphism of an abelian variety induces a decomposition of the variety up to isogeny. There are two such results, namely the isotypical decomposition and Roan’s decomposition theorem. We show that they are essentially the same. Moreover, we generalize in a sense this result to abelian varieties with action of an arbitrary finite abelian group...

Amir-Khosravi, Zavosh
Published in
manuscripta mathematica

Given a polarized abelian scheme with action by a ring, and a projective finitely presented module over that ring, Serre’s tensor construction produces a new abelian scheme. We show that to equip these abelian schemes with polarizations it’s enough to equip the projective modules with non-degenerate positive-definite hermitian forms. As an applicat...

Skryzalin, Jacek Carlsson, Gunnar
Published in
Journal of Applied and Computational Topology

Topological data analysis is the study of data using techniques from algebraic topology. Often, one begins with a finite set of points representing data and a “filter” function which assigns a real number to each datum. Using both the data and the filter function, one can construct a filtered complex for further analysis. For example, applying the ...

Nakayama, Chikara

"Algebraic Number Theory and Related Topics 2014". December 1～5, 2014. edited by Takeshi Tsuji, Hiroki Takahashi and Yuichiro Hoshi. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed. / This is a survey on the theory of log abelian varieties, which is a new formulation of degenerating abelian varieties in...

呼子, 笛太郎

"Algebraic Number Theory and Related Topics 2014". December 1～5, 2014. edited by Takeshi Tsuji, Hiroki Takahashi and Yuichiro Hoshi. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed. / The Eichler-Deuring mass formula says that the weighted number of isomorphism classes of supersingular elliptic curves o...

Frediani, Paola Neumann, Frank
Published in
Journal of Homotopy and Related Structures

We determine the Artin–Mazur étale homotopy types of moduli stacks of polarised abelian schemes using transcendental methods and derive some arithmetic properties of the étale fundamental groups of these moduli stacks. Finally we analyse the Torelli morphism between the moduli stacks of algebraic curves and principally polarised abelian schemes fro...

Jahnke, Priska Radloff, Ivo
Published in
Mathematische Annalen

Projective structures on compact real manifolds are classical objects in real differential geometry. Complex manifolds with a holomorphic projective structure on the other hand form a special class as soon as the dimension is greater than one. In the Kähler Einstein case Pm\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \use...

Ren, Qingchun Sam, Steven V. Sturmfels, Bernd
Published in
Mathematics in Computer Science

The image of the complement of a hyperplane arrangement under a monomial map can be tropicalized combinatorially using matroid theory. We apply this to classical moduli spaces that are associated with complex reflection arrangements. Starting from modular curves, we visit the Segre cubic, the Igusa quartic, and moduli of marked del Pezzo surfaces o...

Tang, Shun
Published in
Manuscripta Mathematica

In this paper we prove a refined version of the canonical key formula for projective abelian schemes in the sense of Moret-Bailly (cf. Astérisque 129, 1985), we also extend this discussion to the context of Arakelov geometry. Precisely, let π:A→S\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackag...