A note on Galois embeddings of abelian varieties

In this note we show that if an abelian variety possesses a Galois embedding into some projective space, then it must be isogenous to the self product of an elliptic curve. We prove moreover that the self product of an elliptic curve always has infinitely many Galois embeddings.Comment: Some typos fixed. To appear in Manuscripta Mathematic

Fixed points of endomorphisms of complex tori

We study the asymptotic behavior of the cardinality of the fixed point set of iterates of an endomorphism of a complex torus. We show that there are precisely three types of behavior of this function: it is either an exponentially growing function, a periodic function, or a product of both.Comment: Some typos corrected; the introduction was also revise

Hopfield Networks in Relevance and Redundancy Feature Selection Applied to Classification of Biomedical High-Resolution Micro-CT Images

We study filter–based feature selection methods for classification of biomedical images. For feature selection, we use two filters — a relevance filter which measures usefulness of individual features for target prediction, and a redundancy filter, which measures similarity between features. As selection method that combines relevance and redundancy we try out a Hopfield network. We experimentally compare selection methods, running unitary redundancy and relevance filters, against a greedy algorithm with redundancy thresholds [9], the min-redundancy max-relevance integration [8,23,36], and our Hopfield network selection. We conclude that on the whole, Hopfield selection was one of the most successful methods, outperforming min-redundancy max-relevance when\ud more features are selected

The Gauss map and secants of the Kummer variety

Fay's trisecant formula shows that the Kummer variety of the Jacobian of a smooth projective curve has a four dimensional family of trisecant lines. We study when these lines intersect the theta divisor of the Jacobian, and prove that the Gauss map of the theta divisor is constant on these points of intersection, when defined. We investigate the relation between the Gauss map and multisecant planes of the Kummer variety as well.Comment: Minor changes, to appear on the Bulletin of London Mathematical Societ

Smooth quotients of abelian surfaces by finite groups

Let $A$ be an abelian surface and let $G$ be a finite group of automorphisms of $A$ fixing the origin. Assume that the analytic representation of $G$ is irreducible. We give a classification of the pairs $(A,G)$ such that the quotient $A/G$ is smooth. In particular, we prove that $A=E^2$ with $E$ an elliptic curve and that $A/G\simeq\mathbb P^2$ in all cases. Moreover, for fixed $E$, there are only finitely many pairs $(E^2,G)$ up to isomorphism. This completes the classification of smooth quotients of abelian varieties by finite groups started by the first two authors.Comment: 15 pages. Comments are welcome. arXiv admin note: text overlap with arXiv:1801.0002

A decomposition of the Jacobian of a Humbert-Edge curve

A \textit{Humbert-Edge curve of type} $n$ is a non-degenerate smooth complete intersection of $n-1$ diagonal quadrics. Such a curve has an interesting geometry since it has a natural action of the group $(\mathbb{Z}/2\mathbb{Z})^n$. We present here a decomposition of its Jacobian variety as a product of Prym-Tyurin varieties, and we compute the kernel of the corresponding isogeny.Comment: 9 pages, comments welcome! To appear in Contemporary Mathematic

Galois subspaces for projective varieties

Given an embedding of a projective variety into projective space, we study the structure of the space of all linear projections that, when composed with the embedding, give a Galois morphism from the variety to a projective space of the same dimension.Comment: 14 pages, any comments welcome

Menschen reisen zu den Göttern, Götter reisen zu den Menschen: Religio migrans in Abonuteichos und am Schwarzen Meer

Three forms of religio migrans (religion on the move) are addressed in this paper: 1. When people migrate to far-off lands, they take their gods with them (‘Gods join migrant people on their journey’). 2. In their new abodes migrant people will confer an allotted place to their gods to dwell together with them; both will integrate into the neighborhood (religio translata). 3. People travel to the gods. Of the three, the third is treated most in-depth. As a point of departure the essay begins with the founding of a new cult in the Roman Empire on the southern coast of the Black Sea: the cult of the New Asklepios Glykon. Taking the narrative of Lucian as part of a persecution speech, it can be seen as a historical source that fits well in the religious history of the mid-2nd century AD. 1) illustrating the spread of the cult in the region of the southwestern coast of the Black Sea and 2) understood as a result of the cult’s attractiveness for the people from the region, who travelled to a god at the heart of a healing and oracle cult and a great festival. I continue to develop the systematic analysis of religio migrans further in respect to 3) religious tourism, pilgrimage, the attractiveness of even remote localities, language diversity, etc. within the framework of religion during the Roman Empire