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Teoría métrica de curvas semialgebráicas.

Lev Birbrair, Alexandre C. G. Fernandes (2000)

Revista Matemática Complutense

We present a complete bi-Lipschitz classification of germs of semialgebraic curves (semialgebraic sets of the dimension one). For this purpose we introduce the so-called Hölder Semicomplex, a bi-Lipschitz invariant. Hölder Semicomplex is the collection of all first exponents of Newton-Puiseux expansions, for all pairs of branches of a curve. We prove that two germs of curves are bi-Lipschitz equivalent if and only if the corresponding Hölder Semicomplexes are isomorphic. We also prove that any Hölder...

The number of conics tangent to five given conics: the real case.

Felice Ronga, Alberto Tognoli, Thierry Vust (1997)

Revista Matemática de la Universidad Complutense de Madrid

It is a classical result, first established by de Jonquières (1859), that generically the number of conics tangent to 5 given conics in the complex projective plane is 3264. We show here the existence of configurations of 5 real conics such that the number of real conics tangent to them is 3264.

The principle of moduli flexibility for real algebraic manifolds

Edoardo Ballico, Riccardo Ghiloni (2013)

Annales Polonici Mathematici

Given a real closed field R, we define a real algebraic manifold as an irreducible nonsingular algebraic subset of some Rⁿ. This paper deals with deformations of real algebraic manifolds. The main purpose is to prove rigorously the reasonableness of the following principle, which is in sharp contrast with the compact complex case: "The algebraic structure of every real algebraic manifold of positive dimension can be deformed by an arbitrarily large number of effective parameters".

Topology of real algebraic T-surfaces.

Ilia Itenberg (1997)

Revista Matemática de la Universidad Complutense de Madrid

The paper is devoted to algebraic surfaces which can be obtained using a simple combinatorial procedure called the T-construction. The class of T-surfaces is sufficiently rich: for example, we construct T-surfaces of an arbitrary degree in RP³ which are M-surfaces. We also present a construction of T-surfaces in RP³ with dim H1 (RX; Z/2) > h1, 1(CX), where RX and CX are the real and the complex point sets of the surface.

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