Luca Chiantini

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INTRODUCTION In this paper we investigate to which extent the theory of Severi on nodal plane curves of a given degree d extends to a linear system on a complex projective nonsingular algebraic surface. As well known, in [S], Anhang F Severi proved that for every d ≥ 3 and 0 ≤ δ ≤ d−1
The geometry of a desingularization Y m of an arbitrary subvariety of a generic hypersurface X n in an ambient variety W (e.g. W = P n+1) has received much attention over the past decade or so. Clemens [CKM] has proved that for m = 1, n = 2, W = P 3 and X of degree d, Y has genus g ≥ 1 + d(d − 5)/2 and Xu [X] improved this to g ≥ d(d − 3)/2 − 2 for d ≥ 5(More)
For an irreducible projective variety X, we study the family of h-planes contained in the secant variety Sec k (X), for 0 < h < k. These families have an expected dimension and we study varieties for which the expected dimension is not attained; for these varieties, making general consecutive projections to lower dimensional spaces, we do not get the(More)
A linear series g N δ on a curve C ⊂ P 3 is primary when it does not contain the series cut by planes. For such series, we provide a lower bound for the degree δ, in terms of deg(C), g(C) and of the number s = min{i : h 0 I C (i) = 0}. Examples show that the bound is sharp. Extensions to the case of general linear series and to the case of curves in higher(More)