arXiv subjects

A. Muhammed Uludag

Publications and source records attributed to A. Muhammed Uludag.

4 recordsLinked to original sources

arXiv2025

Equivariant Modular Functions and Quantizations of Continued Fractions

We show that, in addition to the quantizations of the rational numbers discovered by Morier-Genoud and Ovsienko, there exist a pair of conjugate representations of the modular group and the corresponding equivariant maps with respect to these representations. We discuss some specializations of these quantizations and discuss its connection to Dyer's outer automorphism and the associated involution Jimm of the real line.

math.CO↗

arXiv2006

Smooth finite abelian uniformizations of projective spaces and Calabi-Yau Orbifolds

We give a classification of smooth complex manifolds with a finite abelian group action, such that the quotient is isomorphic to a projective space. The case where the manifold is a Calabi-Yau is studied in detail.

math.AG↗

arXiv2003

Covering relations between ball-quotient orbifolds

Some ball-quotient orbifolds are related by covering maps. We exploit these coverings to find infinite towers of orbifolds uniformized by the complex 2-ball and some orbifolds over K3 surfaces uniformized by the 2-ball. Corresponding lattices are all arithmetic and commensurable. We also give, along with infinitely many reducible examples, an infinite series of irreducible curves along which the projective plane is uniformized by the product of two 1-balls.

math.AG↗

arXiv2003

On Branched Galois Coverings $(B_1)^n\to {\mathbb P}^n$

For any $n>1$, we construct examples branched Galois coverings from $M$ to the nth projective space ${\mathbb P}^n$ where $M$ is one of $({\mathbb P}^1)^n$, ${\mathbb C}^n$ or $(B_1)^n$, and $B_1$ is the 1-ball. In terms of orbifolds, this amounts to giving examples of orbifolds over ${\mathbb P}^n$ uniformized by $M$.We also discuss the related "orbifold braid groups".

math.AG↗