arXiv subjects

Andreas Demleitner

Publications and source records attributed to Andreas Demleitner.

7 recordsLinked to original sources

arXiv2024

The Albanese morphism for hyperelliptic varieties

We explicitly describe the Albanese morphism of a hyperelliptic variety, i.e., the quotient $X$ of an abelian variety $A$ by a finite group $G$ acting freely and not only by translations, by giving a description of the Albanese variety and the Albanese fibers in terms of $A$ and $G$. In particular, the fibers are themselves abelian or hyperelliptic varieties, and we investigate which can occur in explicit examples. As an application we show that the derived category of $X$ is indecomposable in certain cases.

math.AG↗

arXiv2022

The Classification of Hyperelliptic Groups in Dimension 4

Hyperelliptic manifolds are natural generalizations of hyperelliptic surfaces in dimensions. We provide a full classification of the groups, which arise as the holonomy group of a 4-dimensional hyperelliptic manifold. The classification is mostly based on group- and representation-theoretic methods.

math.AG↗

arXiv2022

The Classification of Rigid Hyperelliptic Fourfolds

We provide a fine classification of rigid hyperelliptic manifolds in dimension four up to biholomorphism and diffeomorphism. These manifolds are explicitly described as finite \'etale quotients of a product of four Fermat elliptic curves.

math.AG↗

arXiv2019

Rigid Group Actions on Complex Tori are Projective (after Ekedahl)

In this note we give a detailed proof of a result (sketched by Torsten Ekedahl in a discussion with the first author several years ago), describing complex tori admitting a rigid group action and showing explicitly their projectivity and their structure in terms of CM-fields. In the appendix, joint with Benoit Claudon, we show, using a method of Green-Voisin, that all group actions on complex tori deform to projective ones.

math.AG↗

arXiv2018

The classification of Hyperelliptic threefolds

We complete the classification of hyperelliptic threefolds, describing in an elementary way the hyperelliptic threefolds with group $D_4$. These are algebraic and form an irreducible 2-dimensional family. Our paper is fully self-contained.

math.AG↗

arXiv2018

Hyperelliptic Threefolds with group $D_4$, the Dihedral group of order 8

We give a simple construction for the hyperelliptic threefolds with group $D_4$, thus completing the classification of hyperelliptic threefolds.

math.AG↗

arXiv2017

Classification of Bagnera-de Franchis Varieties in Small Dimensions

A Bagnera-de Franchis variety $X = A/G$ is the quotient of an abelian variety $A$ by a free action of a finite cyclic group $G \subset Bihol(A)$, which does not contain only translations. Constructing explicit polarizations and using a method introduced by F. Catanese, we classify split Bagnera-de Franchis varieties up to complex conjugation in dimensions $\leq 4$.

math.AG↗