Let p be a prime number and f ∈ Zp[x] a polynomial over the p-adic integers lifting the Frobenius in the sense that f(x) ≡ xp (mod p) and deg(f) = p. Let Πf := {ζ ∈ Q p : f◦n(ζ) = ζ for some n ∈ Z+} be the set of f -periodic points. We show that an irreducible algebraic varieties X ⊆ Am which meet Γ×m f in a Zariski dense set only in the case that X is defined by equations of the form xi = a fo...

An overview of the braid group techniques in the theory of algebraic surfaces from Zariski to the latest results is presented. An outline of the Van Kampen algorithm for computing fundamental groups of complements of curves and the modification of Moishezon-Teicher regarding branch curves of generic projections are given. The paper also contains a description of a quotient of the braid group, n...

In this paper‎, ‎we mainly investigate how the generalized metrizability properties of the remainders affect the metrizability of rectifiable spaces‎, ‎and how the character of the remainders affects the character‎ ‎and the size of a rectifiable space‎. ‎Some results in [A. V‎. ‎Arhangel'skii and J‎. ‎Van Mill‎, ‎On topological groups with a first-countable remainder‎, ‎Topology Proc. 42 (2013...

We show that two analytic function germs (C, 0) → (C, 0) are topologically right equivalent if and only if there is a one-to-one correspondence between the irreducible components of their zero sets that preserves the multiplicites of these components, their Puiseux pairs, and the intersection numbers of any pairs of distinct components. By Zariski [10] and Burau [2], the topological type of an ...

Let R be a commutative hyperring with identity. We introduceand study prime fuzzy hyperideals of R. We investigate the Zariski topologyon FHspec(R), the spectrum of prime fuzzy hyperideals of R.

We relate closure operations for ideals and for submodules to non-flat Grothendieck topologies. We show how a Grothendieck topology on an affine scheme induces a closure operation in a natural way, and how to construct for a given closure operation fulfilling certain properties a Grothendieck topology which induces this operation. In this way we relate the radical to the surjective topology and...

We study linear subspaces L ⊆ Mn (over an algebraically closed field F of characteristic zero) and their singular sets S(L) defined by S(L) = {A ∈ Mn : χ(A+ L) is not dense in Fn}, where χ : Mn −→ F n is the characteristic map. We give a complete characterization of the subspaces L ⊂ M2 such that ∅ 6= S(L) 6= M2. We also provide a complete characterization of the singular sets S(L) in the case ...

Abstract We will describe the topological type of discriminant curve morphism $$(\ell , f)$$ ( ℓ , f ) where $$\ell $$ is a smooth and f an irreducible (branch) multiplicity less than five or branch such that difference...

Let G be a reductive algebraic group over an algebraically closed field k. An algebraic characteristic class of degree i for principal G-bundles on schemes is a function c assigning to each principal G-bundle E → X an element c(E) in the Chow group AX, natural with respect to pullbacks. These classes are analogous to topological characteristic classes (which take values in cohomology), and two ...