Given a compact affine nonsingular real algebraic variety X and a nonsingular subvariety Z C X belonging to a large class of subvarieties, we show how to embed X in a suitable Grassmannian so that Z becomes the transverse intersection of the zeros of a section of the tautological bundle on the Grassmannian.
We use floor decompositions of tropical curves to prove that any enumerative problem concerning conics passing through projective-linear subspaces in is maximal. That is, there exist generic configurations of real linear spaces such that all complex conics passing through these constraints are actually real.
We give a criterion for a real-analytic function defined on a compact nonsingular real algebraic set to be analytically equivalent to a rational function.
We prove the rationality of the Łojasiewicz exponent for semialgebraic functions without compactness hypothesis. In the parametric situation, we show that the parameter space can be divided into a finite number of semialgebraic sets on each of which the Łojasiewicz exponent is constant.
There is a well-known procedure -induction- for extending an action of a subgroup H of a Lie group G on a topological space X to an action of G on an associated space. Induction can also extend a smooth action of a subgroup H of a Lie group G on a manifold M to a smooth action of G on an associated manifold. In this paper elementary methods are used to show that induction also works in the category of (nonsingular) real algebraic varieties and regular or entire maps if G is a compact abelian Lie...