527 research outputs found
Plucker-Clebsch formula in higher dimension
Let S\subset\Ps^r () be a nondegenerate, irreducible, smooth,
complex, projective surface of degree . Let be the number of
double points of a general projection of to \Ps^4. In the present paper
we prove that , with equality if and only if
is a rational scroll. Extensions to higher dimensions are discussed.Comment: 12 page
On the topology of a resolution of isolated singularities
Let be a complex projective variety of dimension with isolated
singularities, a resolution of singularities,
the exceptional locus. From Decomposition Theorem
one knows that the map
vanishes for . Assuming this vanishing, we give a short proof of
Decomposition Theorem for . A consequence is a short proof of the
Decomposition Theorem for in all cases where one can prove the vanishing
directly. This happens when either is a normal surface, or when is
the blowing-up of along with smooth and connected fibres,
or when admits a natural Gysin morphism. We prove that this last
condition is equivalent to say that the map vanishes for any , and that the pull-back
is injective. This provides a relationship between
Decomposition Theorem and Bivariant Theory.Comment: 18 page
N\'eron-Severi group of a general hypersurface
In this paper we extend the well known theorem of Angelo Lopez concerning the
Picard group of the general space projective surface containing a given smooth
projective curve, to the intermediate N\'eron-Severi group of a general
hypersurface in any smooth projective variety.Comment: 14 pages, to appear on Communications in Contemporary Mathematic
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