We give a complete (global) characterization of $${\mathbb {C}}$$ -perverse sheaves on semi-abelian varieties in terms their cohomology jump loci. Our results generalize Schnell’s work perverse complex abelian varieties, as well Gabber–Loeser’s affine tori. apply our to the study loci smooth quasi-projective topology Albanese map, and context homological duality properties algebraic varieties.

Iteration of randomly chosen quadratic maps defines a Markov process: Xn+1 = εn+1Xn(1−Xn), where εn are i.i.d. with values in the parameter space [0,4] of quadratic maps Fθ(x) = θx(1− x). Its study is of significance as an important Markov model, with applications to problems of optimization under uncertainty arising in economics. In this article a broad criterion is established for positive Ha...

We analyze mass linear functions on simple polytopes ∆, where a mass linear function is an affine function on ∆ whose value on the center of mass depends linearly on the positions of the supporting hyperplanes. On the one hand, we show that certain types of symmetries of ∆ give rise to nonconstant mass linear functions on ∆. We call mass linear functions which arise in this way inessential; the...

the subgroups of symplectic groups which fix a non-zero vector of the underlying symplectic space are called affine subgroups., the split extension group $a(4)cong 2^7{:}sp_6(2)$ is the affine subgroup of the symplectic group $sp_8(2)$ of index $255$‎. ‎in this paper‎, ‎we use the technique of the fischer-clifford matrices to construct the character table of the inertia group $2^7{:}o^{-}_{6}(2...

Explicit formulas are obtained for the number of periodic points and maximum tail length split polynomial maps over finite fields affine projective space. This work includes a detailed analysis structure directed graph Chebyshev polynomials non-prime degree in dimension 1 powering map any dimension. The results applied to an algorithm determining type given through its cycle statistics modulo p...

We establish the sharp rate of continuity extensions ℝm-valued 1-Lipschitz maps from a subset A ℝn to on ℝn. consider several cases when there exists extension with preserved uniform distance given map. prove that if m > 1, then map is and affine only such preserving for any defined This shows striking difference case = where function has property. Another example we it possible find an same Li...

Let I be an ideal of the polynomial ring A[x] = A[x1, . . . , xn] over the commutative, noetherian ring A. Geometrically I defines a family of affine schemes over Spec(A): For p ∈ Spec(A), the fibre over p is the closed subscheme of affine space over the residue field k(p), which is determined by the extension of I under the canonical map σp : A[x] → k(p)[x]. If I is homogeneous there is an ana...

Let M be a compact connected Fujiki manifold, G semisimple affine algebraic group over C with one simple factor and P fixed proper parabolic subgroup of G. For holomorphic principal G–bundle EG M, let EP the P–bundle EG⟶EG/P given by quotient map. We prove that following three statements are equivalent: (1) ad(EG) is numerically flat, (2) line bundle ⋀topad(EP)⁎ nef, (3) for every reduced irred...

the subgroups of symplectic groups which fix a non-zero vector of the underlying symplectic space are called emph{affine subgroups.}~the split extension group $a(4)cong 2^7{:}sp_6(2)$ is the affine subgroup of the symplectic group $sp_8(2)$ of index $255$‎. ‎in this paper‎, ‎we use the technique of the fischer-clifford matrices to construct the character table of the inertia group $2^7{:}o^{-}_...