Alessandro Tancredi

POSITIVE VECTOR BUNDLES ON COMPLEX SURFACES

A criterion for the positivity of a semi-stable vector bundle of rank 2 on a projective surface is proved. This is of particular interest for cotangent bundles of surfaces.

Some remarks on the semi-local extension of Nash maps

SuntoSi studia il problema dellcestensione, in un intorno di un compatto, delle funzioni di Nash da un sottoinsieme di Nash.AbstractThe paper deals with the extension of Nash maps off Nash subvarieties on a neighborhood of a compact set.

On the products of Nash subvarieties by spheres

We show that the product of any sphere by any compact connected component of a real algebraic variety is Nash isomorphic to a real algebraic variety, and we deduce such a result for some non-compact components, too. It follows also that the product of any sphere by any compact global Nash subvariety of R n is Nash isomorphic to a real algebraic variety.

Sulla complessificazione degli spazi di Nash

SummaryWe study the complexification of a real Nash space and its associated analytic structure. Some examples stressing the differences between Nash and analytic complexifications are given.

Algebraicity of Nash sets and of their asymmetric cobordism

This paper deals with the existence of algebraic structures on compact Nash sets. We introduce the algebraic-topological notion of asymmetric Nash cobordism between compact Nash sets, and we prove that a compact Nash set is semialgebraically homeomorphic to a real algebraic set if and only if it is asymmetric Nash cobordant to a point or, equivalently, if it is strongly asymmetric Nash cobordant to a real algebraic set. As a consequence, we obtain new large classes of compact Nash sets semialgebraically homeomorphic to real algebraic sets. To prove our results, we need to develop new algebraic-topological approximation procedures. We conjecture that every compact Nash set is asymmetric Nash cobordant to a point, and hence semialgebraically homeomorphic to a real algebraic set.

Un'osservazione sui sottoinsiemiC-analitici

RiassuntoSi dà una caratterizzazione dei sottoinsiemiC-analitici di un insieme analitico reale coerente.SummaryA characterization ofC-analytic subsets of a coherent real analytic set is given

Compatti olomorficamente convessi di uno spazio analitico

RiassuntoIn questo lavoro si considerano sottoinsiemi compatti olomorficamente convessi di uno spazio analitico non ridotto e si prova che questi sono caratterizzati, come nel caso ridotto, dagli analoghi dei teoremiA eB di Cartan. Si dà inoltre una caratterizzazione di certi morfismi in un compatto olomorficamente convesso.SummaryIn this paper we consider compact holomorphically convex subsets of a non reduced analytic space and we prove that they are characterized, as in the reduced case, by the analogous of Cartans theoremsA andB. We give also a characterization of some morphisms in a compact holomorphically convex set.

Su alcuni funtori rappresentabili in una categoria di spazi analitici relativi

RiassuntoIn questo lavoro si dimostra la rappresentabilità di alcuni funtori che si presentano nella teoria degli spazi analitici relativi sopra uno spazio olomorfo fissato.SummaryIn this paper we prove the representability of some functors occurring in the theory of relative analytic spaces over a fixed holomorphic space.