Let X be a nonsingular quasi-projective complex algebraic variety and let E be an algebraic vector bundle on X of rank r ≥ 2. The pullback of E by the blowup of X at a suitably chosen nonsingular subvariety of X of codimension ...

Let X be an algebraic subset of Rⁿ, and ƒ: X → R a semialgebraic function. We prove that if ƒ is continuous rational on each curve C ⊂ X then: 1) ƒ is arc-analytic, 2) ƒ is continuous rational on X. As a consequence we ...