We construct a relative Chow-Künneth decomposition for a conic bundle over a surface such that the middle projector gives the Prym variety of the associated double covering of the discriminant of the conic bundle. This gives a refinement (up to an isogeny) of Beauville’s theorem on the relation between the intermediate Jacobian of the conic bundle and the Prym variety of the double covering.

In this paper, we prove that f is an 1-sequence-covering (resp., 2sequence-covering) mapping from a locally separable metric space M onto a space X if and only if {(Xλ, {Pλ,n}) : λ ∈ Λ} is a double point-star wsn-cover (resp., double point-star so-cover) for X, where (f,M,X, {Pλ,n}) is an ls-Ponomarevsystem, and investigate further properties of mappings in the ls-Ponomarevsystem (f,M,X, {Pλ,n}).

In digital-based information boom, the fuzzy covering rough set model is an important mathematical tool for artificial intelligence, and how to build the bridge between the fuzzy covering rough set theory and Pawlak’s model is becoming a hot research topic. In this paper, we first present the γ−fuzzy covering based probabilistic and grade approximation operators and double-quantitative approxim...

We consider definably compact groups in an o-minimal expansion of a real closed field. It is known that to each such group G is associated a natural exact sequence 1→ G00 → G → G/G00 → 1 where G00 is the “infinitesimal subgroup” of G and G/G00 is a compact real Lie group. We show that given a connected open subset U of G/G00 there is a canonical isomorphism between the fundamental group of U an...

The double-covering map udc : R 2 → R is given by udc(x) = 1 √ 2|x| ( x2 2 − x12 2x1x2 ) in cartesian coordinates. This paper examines the conjecture that udc is the global minimizer of the Dirichlet energy I(u) = ∫ B |∇u| dx among allW 1,2 mappings u of the unit ball B ⊂ R satisfying (i) u = udc on ∂B, and (ii) det∇u = 1 almost everywhere. Let the class of such admissible maps be A. The chief ...

We investigate the properties of algebraic gamma monomials— that is, algebraic numbers which are expressible as monomials in special values of the classical gamma function. Recently Anderson has constructed a double complex SK, to compute H∗(±,U), where U is the universal ordinary distribution. We use the double complex to deduce explicit formulae for algebraic gamma monomials. We provide simpl...

Given a vector space V and a non-singular quadratic form Q on V , the orthogonal group O(Q) is the subgroup of GL(V ) that preserves Q. The special orthogonal group SO(Q) is given by O(Q) ∩ SL(V ). If Q is the standard inner product on R then SO(Q) is denoted SO(n). This is a connected, compact Lie group. For n > 2, the group is semi-simple. In the case that n is odd, SO(n) corresponds to the D...