Approximation theorems and Nash conjecture
Un teorema di unicità per le teorie dell'omologia
Topological manifolds and real algebraic geometry
We study the problem of approximating, up to homotopy, compact topological manifolds by real algebraic varieties. As a consequence, we realize any integral non-degenerate quadratic form as the intersection form of a real algebraic variety. This is related to a well-known result, due to Freedman [F], on the topology of closed simply-connected topological -manifolds.
Un teorema di approssimazione relativo
Let be an open set of and a real, coherent analytic set. Suppose that be a function such that is analytic. In this paper we want to prove that may be approached (in sense of Whitney’s theorem) by analytic functions such that
Some basic facts in algebraic geometry on a non algebraically closed field
On the analytic approximation of differentiable functions from above
We determine conditions in order that a differentiable function be approximable from above by analytic functions, being left invariate on a fixed analytic subset which is a locally complete intersection.
A note on global Nash subvarieties and Artin-Mazur theorem
It is shown that every connected global Nash subvariety of is Nash isomorphic to a connected component of an algebraic variety that, in the compact case, can be chosen with only two connected components arbitrarily near each other. Some examples which state the limits of the given results and of the used tools are provided.
On the relative Nash approximation of analytic maps.
Proprietà topologiche e topologie iniziali
Let be a set, a topology on is completely regular if, and only if, is the topology defined by a family of maps . It is not difficult to prove that in some sense is minimal under this condition. The purpose of this paper is to characterize the spaces of values that are minimal and the families of topologies on that are complete under the property of being induced by a family of maps .
Alcune proprietà degli spazi quasi algebrici
A q-algebraic function is an analytic function that is in the algebraic closure of the ring of polynomials. In this work we study the q-algebraic spaces (i.e. the ringed spaces that locally are isomorphic to the locus of zeros of a finite number of q-algebraic functions) and we prove, for instance, that any q-algebraic, compact, connected manifold of is homogeneous (in the q-algebraic sense).
Alcune proprietà delle varietà algebriche reali
This work lists some general results about the study of real algebraic varieties (in the sense of Serre). The proofs will appear soon.
The number of conics tangent to five given conics: the real case.
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.
Sull'insieme di non coerenza di un insieme analitico reale
In this short paper we show that the set of points in which a real analytic space is not coherent may be not analytic. (In [2] it is proved that it is always semianalytic).
Sulla non validità di un teorema di approssimazione
The following theorem is true: if is open in , is a coherent real analytic set, and is a function such that is analytic, then it is possible to approximate (together with its derivatives) by analytic functions such that . In this paper we prove that this result is not true unless is coherent (with the reduced structure).
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