相关论文: Fundamental groups of symmetric sextics. II

We compute the homotopy type of the moduli space of flat, unitary connections over aspherical surfaces, after stabilizing with respect to the rank of the underlying bundle. Over the orientable surface M^g, we show that this space has the…

We give a concrete characterization of the rational conjugacy classes of maximal tori in groups of type $D_n$, with specific emphasis on the case of number fields and p-adic fields. This includes the forms associated to quadratic spaces,…

We give a complete classification of complex Q-homology projective planes with isolated rational double point singularities and numerically trivial canonical bundle. There are 31 types, and each has one-dimensional moduli. In fact, all…

Here we initiate a program to study relationships between finite groups and arithmetic-geometric invariants in a systematic way. To do this we first introduce a notion of optimal module for a finite group in the setting of holomorphic mock…

We investigate positive-dimensional closed reductive subgroups of almost simple algebraic groups containing a regular unipotent element. Our main result states that such subgroups do not lie inside proper parabolic subgroups unless possibly…

Magnetic vortices and skyrmions are typically characterized by distinct topological invariants. This work presents a unified approach for the topological classification of these textures, encompassing isolated objects and configurations…

We find a recursive algorithm for computing the precise centralizers of the complex orthogonal and symplectic groups, and hence the isotropy groups, with respect to the similarity transformation on the spaces of skew-symmetric and…

We present a preliminary investigation of algebraic surfaces that have non-planar degenerations, along with their Galois covers and fundamental groups. Specifically, we investigate the tetrahedron and the double tetrahedron. The resulting…

It is one of the wonderful ``coincidences'' of the theory of finite groups that the simple group G of order 25920 arises as both a symplectic group in characteristic 3 and a unitary group in characteristic 2. These two realizations of G…

We compute the rank of the fundamental group of an arbitrary connected component of the space map(X, Y) for X and Y nilpotent CW complexes with X finite. For the general component corresponding to a homotopy class f : X --> Y, we give a…

We describe a combinatorial model for the complement of a complexified toric arrangement by using nerves of acyclic categories. This generalizes recent work of Moci and Settepanella on thick toric arrangements. Moreover, we compute its…

Curve singularities are classical objects of study in algebraic geometry. The key player in their combinatorial structure is the {\it value semigroup}, or its compactification, the {\it value semiring}. One natural problem is to explicitly…

Our main goal is to determine, under certain restrictions, the maximal closed connected subgroups of simple algebraic groups containing a regular torus. We call a torus regular if its centralizer is abelian. We also obtain some results of…

In a step towards the classification of endotrivial modules for quasi-simple groups, we investigate endotrivial modules for the sporadic simple groups and their covers. A main outcome of our study is the existence of torsion endotrivial…

We compute the fundamental group of the Galois cover of a surface of degree~$8$, with singularities of degree $4$, whose degeneration envelope is isomorphic to an octahedron. The group is shown to be a metabelian group of order $2^{23}$.…

We recursively determine the homotopy type of the space of any irreducible framed link in the 3-sphere, modulo rotations. This leads us to the homotopy type of the space of any knot in the solid torus, thus answering a question posed by…

We prove that the moduli space of numerical Godeaux surfaces with torsion group $\mathbb{Z}/2$ is irreducible and unirational of dimension 8. Moreover, we show that the topological fundamental group of these surfaces is also $\mathbb{Z}/2$.…

We study complex plane projective sextic curves with simple singularities up to equisingular deformations. It is shown that two such curves are deformation equivalent if and only if the corresponding pairs are diffeomorphic. A way to…

We make cohomological computations related to the moduli space of genus three curves with symplectic level two structure by means of counting points over finite fields. In particular, we determine the cohomology groups of the quartic locus…

This paper is the first part of a series of three papers about the fundamental groups of conic-line arrangements consist of two tangented conics and up to two additional tangented lines. In this part, we compute the local braid monodromies…