The result of [6] is the existence of an infinite family of Zariski dense surface subgroups of fixed genus inside SL(3,Z); here we exhibit such subgroups inside SL(4,Z) and symplectic groups. In this setting the power of such a result comes in large part from the conclusion that the groups are Zariski dense the existence of surface groups inside SL(4,Z) can be proved fairly easily, since it’s n...

Let X = C. In this paper we present an algorithm that computes the de Rham cohomology groups H dR(U, C) where U is the complement of an arbitrary Zariski-closed set Y in X . Our algorithm is a merger of the algorithm given by T. Oaku and N. Takayama ([7]), who considered the case where Y is a hypersurface, and our methods from [9] for the computation of local cohomology. We further extend the a...

Abstract The group $G = \textrm{GL}_r(k) \times (k^\times )^n$ acts on $\textbf{A}^{r n}$, the space of $r$-by-$n$ matrices: $\textrm{GL}_r(k)$ by row operations and $(k^\times scales columns. A matrix orbit closure is Zariski a point for this action. We prove that class such an in $G$-equivariant $K$-theory n}$ determined matroid generic point. present two formulas class. key to proof show clo...

for the first time in the minkowski space, an rn 1 time-like complementary ruled surface isdescribed and relations are given connected with an asymptotic and tangential bundle of the time-likecomplementary ruled surface. furthermore, theorems are given related to edge space, central space andcentral ruled surface of this complementary ruled surface.

The main result of this article is a refinement of the well-known subgroup separability results of Hall and Scott for free and surface groups. We show that for any finitely generated subgroup, there is a finite dimensional representation of the free or surface group that separates the subgroup in the induced Zariski topology. As a corollary, we establish a polynomial upper bound on the size of ...

We study Zariski pairs of sextics which are distinguished by the Alexander polynomials. For this purpose, we present two constructive methods to produce explicit sextics of non-torus type with given configuration of simple singularities.