Related papers: The Degrees Of Toroidal Regular Proper Hypermaps

Classically, regular homomorphisms have been defined as a replacement for Abel--Jacobi maps for smooth varieties over an algebraically closed field. In this work, we interpret regular homomorphisms as morphisms from the functor of families…

We find sharp upper bounds on the order of the automorphism group of a hypersurface in complex projective space in every dimension and degree. In each case, we prove that the hypersurface realizing the upper bound is unique up to…

The necessary and sufficient conditions for a three-dimensional Riemannian metric to admit a transitive group of isometries are obtained. These conditions are Intrinsic, Deductive, Explicit and ALgorithmic, and they offer an IDEAL labeling…

Given an arrangement of subtori of arbitrary codimension in a torus, we compute the cohomology groups of the complement. Then, using the Leray spectral sequence, we describe the multiplicative structure on the graded cohomology. We also…

We completely determine cohomology groups of sections of homogeneous line bundles over a toroidal group.

The genus spectrum of a finite group $G$ is the set of all $g\geq 2$ such that $G$ acts faithfully and orientation-preserving on a closed compact orientable surface of genus $g$. This article is an overview of some results relating the…

We contribute to the classification of toroidal circle planes and flat Minkowski planes possessing three-dimensional connected groups of automorphisms. When such a group is an almost simple Lie group, we show that it is isomorphic to…

In this dissertation, we explore the structure of inversion graphs of permutations--a class of graphs that naturally arises by representing each permutation as a graph, where vertices correspond to entries and edges encode inversions.…

We study a certain family of simple fusion systems over finite $3$-groups, ones that involve Todd modules of the Mathieu groups $2M_{12}$, $M_{11}$, and $A_6=O^2(M_{10})$ over $\mathbb{F}_3$, and show that they are all isomorphic to the…

We classify homomorphisms from mapping class groups by using finite subgroups. First, we give a new proof of a result of Aramayona--Souto that homomorphisms between mapping class groups of closed surfaces are trivial for a range of genera.…

For all Frobenius groups and a large class of finite multiply transitive permutation groups, we show that the corresponding group-subgroup subfactors are completely characterized by their principal graphs. The class includes all the sharply…

We show that there are a finite number of possible pictures for a surface in a tetrahedron with local index $n$. Combined with previous results, this establishes that any topologically minimal surface can be transformed into one with a…

The modular variety of non singular and complete hyperelliptic curves with level-two structure of genus 3 is a 5-dimensional quasi projective variety which admits several standard compactifications. The first one, X, comes from the…

In this paper, we construct polynomial growth harmonic maps from once-punctured Riemann surfaces of any finite genus to any even-sided, regular, ideal polygon in the hyperbolic plane. We also establish their uniqueness within a class of…

We classify surface Houghton groups, as well as their pure subgroups, up to isomorphism, commensurability, and quasi-isometry.

Fix a degree $d$ projective curve $X \subset \mathbb{P}^r$ over an algebraically closed field $K$. Let $U \subset (\mathbb{P}^r)^*$ be a dense open subvariety such that every hyperplane $H \in U$ intersects $X$ in $d$ smooth points. Varying…

Let $g\geq3$ and $n\geq0$, and let ${\mathcal{M}}_{g,n}$ be the mapping class group of a surface of genus $g$ with $n$ boundary components. We prove that ${\mathcal{M}}_{g,n}$ contains a unique subgroup of index $2^{g-1}(2^{g}-1)$ up to…

There exists a covariant non-injective functor from the space of generic Riemann surfaces to the so-called toric AF-algebras; such a functor maps isomorphic Riemann surfaces to the stably isomorphic toric AF-algebras. We use the functor to…

This paper presents new examples of projective surfaces of general type over $\mathbb{C}$ with canonical map of degree $ 3 $ onto a surface of general type. Very few examples are known of such surfaces and some of the examples in this paper…

We construct a model of the Hermitian unital of order 3 (obtained from the non-degenerate hermitian form in three variables over the field of order 9) inside the octonion algebra over the field of order 2. This construction is invariant…