Related papers: Arithmetic Monodromy Groups of Dynamical Belyi map…

In this article, we study the properties of profinite geometric iterated monodromy groups associated to polynomials. Such groups can be seen as generic representations of absolute Galois groups of number fields into the automorphism group…

We explore the enumerative problem of finding lines on cubic surfaces defined by symmetric polynomials. We prove that the moduli space of symmetric cubic surfaces is an arithmetic quotient of the complex hyperbolic line, and determine…

We describe all possible coactions of finite groups (equivalently, all group gradings) on two-dimensional Artin-Schelter regular algebras. We give necessary and sufficient conditions for the associated Auslander map to be an isomorphism,…

The finite monodromy groups of abelian varieties over number fields have been introduced by Grothendieck. They represent the local obstruction to semi-stable reduction. In this paper we prove a criteria for finite groups to be realized as…

We investigate monodromy groups arising in enumerative geometry, with a particular focus on how these groups are influenced by prescribed symmetries. To study these phenomena effectively, we work in the framework of moduli stacks rather…

This paper investigates the relationship between strata of abelian differentials and various mapping class groups afforded by means of the topological monodromy representation. Building off of prior work of the authors, we show that the…

We consider quotients of the group algebra of the $3$-string braid group $B_3$ by $p$-th order generic polynomial relations on the elementary braids. In cases $p=2,3,4,5$ these quotient algebras are finite dimensional. We give…

We study the postcritically finite non-polynomial map $f(x)=\frac{1}{(x-1)^2}$ over a number field $k$ and prove various results about the geometric $G^{\text{geom}}(f)$ and arithmetic $G^{\text{arith}}(f)$ iterated monodromy groups of $f$.…

We study the Schwarz maps with monodromy groups isomorphic to the triangle groups (2,4,4) and (2,3,6) and their inverses. We apply our formulas to the study of mean iterations.

We give a sufficient condition on a pair of (primitive) integral polynomials that the associated hypergeometric group (monodromy group of the corresponding hypergeometric differential equation) is an arithmetic subgroup of the integral…

One of the toughest problems in Ramsey theory is to determine the existence of monochromatic arithmetic progressions in groups whose elements have been colored. We study the harder problem to not only determine the existence of…

One studies Cremona monomial maps by combinatorial means. Among the results is a simple integer matrix theoretic proof that the inverse of a Cremona monomial map is also defined by monomials of fixed degree, and moreover, the set of…

Every smooth minimal complex algebraic surface of general type, $X$, may be mapped into a moduli space, $\MM_{c_1^2(X), c_2(X)}$, of minimal surfaces of general type, all of which have the same Chern numbers. Using the braid group and braid…

We study Witt groups of smooth curves and surfaces over algebraically closed fields of characteristic not two. In both dimensions, we determine both the classical Witt group and Balmer's shifted Witt groups. In the case of curves, the…

We prove that the symmetric monoidal category of mixed motives generated by an abelian variety (more generally, an abelian scheme) can be described as a certain module category. More precisely, we describe it as the category of…

We describe a 3-step filtration on all logarithmic abelian varieties with constant degeneration. The obstruction to descending this filtration, as a variegated extension, from logarithmic geometry to algebraic geometry is encoded in a…

The bigraded Betti numbers b^{-i,2j}(P) of a simple polytope P are the dimensions of the bigraded components of the Tor groups of the face ring k[P]. The numbers b^{-i,2j}(P) reflect the combinatorial structure of P as well as the topology…

We present a genus 0 Belyi map for the sporadic Janko group J2 of degree 280. As a consequence we obtain a polynomial having Aut(J2) as a Galois group over K(t) where K is a number field of degree 10.

We construct Belyi maps having specified behavior at finitely many points. Specifically, for any curve C defined over Q-bar, and any disjoint finite subsets S, T in C(Q-bar), we construct a finite morphism f: C -> P^1 such that f ramifies…

Abelian groups having partial orderings compatible with their binary operations have long been studied in the literature. In particular, lattice-ordered abelian groups constitute a universal-algebraic variety, and thus form a category which…