Rational quartic spectrahedra in $3$-space are semialgebraic convex subsets $\mathbb{R} ^3$ of semidefinite, real symmetric $(4 \times 4)$-matrices, whose boundary admits a rational parameterization. The Zariski closure $\mathbb{C}\mathbb{P} the spectrahedron is complex symmetroid. We give necessary conditions on configurations singularities corresponding symmetroids \mathbb{P} spectrahedra. pr...

Abstract Let $\Gamma $ be a Zariski dense Anosov subgroup of connected semisimple real algebraic group $G$. For maximal horospherical $N$ $G$, we show that the space all non-trivial $NM$-invariant ergodic and $A$-quasi-invariant Radon measures on \backslash G$, up to proportionality, is homeomorphic ${\mathbb {R}}^{\text {rank}\,G-1}$, where $A$ split torus $M$ compact normalizes $N$. One main ...

— In this paper we show how to recover a special class of valuations (which generalize in a natural way the Zariski prime divisors) of function fields from the Galois theory of the functions fields in discussion. These valuations play a central role in the birational anabelian geometry and related questions. Résumé (Théorie de Galois pro-` des diviseurs premiers de Zariski) Dans cet article nou...

We give a cohomological characterization of semiample line bundles. The result is a common generalization of the Fujita-Zariski Theorem on semiampleness and the Grothendieck-Serre criterion for ampleness. As an application of the Fujita-Zariski Theorem we characterize contractible curves in 1-dimensional families.

In this paper, we define the concept of probabilistic like Menger (probabilistic like quasi Menger) space (briefly, PLM-space (PLqM-space)). We present some coupled fixed point and fixed point results for certain contraction type maps in partially order PLM-spaces (PLqM- spaces).

Many of the stochastic models used in inference of phylogenetic trees from biological sequence data have polynomial parameterization maps. The image of such a map—the collection of joint distributions for all parameter choices—forms the model space. Since the parameterization is polynomial, the Zariski closure of the model space is an algebraic variety which is typically much larger than the mo...

Let G be a semi-simple Lie group and Γ < G be a lattice. This paper is motivated by the attempt to understand the infinite index subgroup structure of Γ . In particular, to understand the possibilities for infinite index, finitely generated, freely indecomposable, Zariski dense subgroups of Γ . The study of Zariski dense subgroups of semi-simple Lie groups has a long and rich history. Some high...

In the classical case all unirational surfaces are rational. This was rst realized by Oscar Zariski ((20], p. 314). Prompted by Hironaka's suggestion, we began an investigation of the type of surfaces introduced by Zariski in that paper. The research was originally begun by Blass in 1970-71 at Harvard with the advice of Hironaka and Zariski, and then during 1974{1977 he continued under the dire...

For a module M over commutative ring R with identity, let RSpec(M) denote the collection of all submodules L Msuch that ?(L:M) is prime ideal and equal to (rad L:M). In this article, we topologies topology which enjoys analogs many properties Zariski on spectrum Spec(M) (as subspace topology). We investigate topological space from point view spectral spaces by establishing interrelations betwee...