ﻻ يوجد ملخص باللغة العربية
Let $X$ be an algebraic surface of degree $5$, which is considered as a branch cover of $mathbb{CP}^2$ with respect to a generic projection. The surface has a natural Galois cover with Galois group $S_5$. In this paper, we deal with the fundamental groups of Galois covers of degree $5$ surfaces that degenerate to nice plane arrangements; each of them is a union of five planes such that no three planes meet in a line.
In this paper we consider the Galois covers of algebraic surfaces of degree 6, with all associated planar degenerations. We compute the fundamental groups of those Galois covers, using their degeneration. We show that for 8 types of degenerations the
Let $X$ be a smooth projective connected curve of genus $gge 2$ defined over an algebraically closed field $k$ of characteristic $p>0$. Let $G$ be a finite group, $P$ a Sylow $p$-subgroup of $G$ and $N_G(P)$ its normalizer in $G$. We show that if the
We explain how to reconstruct the category of Artin-Tate $mathbb{R}$-motivic spectra as a deformation of the purely topological $C_2$-equivariant stable category. The special fiber of this deformation is algebraic, and equivalent to an appropriate ca
In this article, we show that for any non-isotrivial family of abelian varieties over a rational base with big monodromy, those members that have adelic Galois representation with image as large as possible form a density-$1$ subset. Our results can
In this paper, we develop and study the theory of weighted fundamental groups of weighted simplicial complexes. When all weights are 1, the weighted fundamental group reduces to the usual fundamental group as a special case. We also study weight