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- Luca Chiantini, Carlo Madonna
- 2004

In this paper we show that on a general sextic hypersurface X ⊂ P 4 , a rank 2 vector bundle E splits if and only if h 1 (E(n)) = 0 for any n ∈ Z. We get thus a characterization of complete intersection curves in X.

- L Chiantini, E Sernesi
- 1996

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

- Luca Chiantini, Carlo Madonna
- 2001

We give a partial positive answer to a conjecture of Tyurin ([28]). Indeed we prove that on a general quintic hypersurface of P 4 every arithmetically Cohen–Macaulay rank 2 vector bundle is infinitesimally rigid.

- L Chiantini, C Madonna
- 2004

In this paper we show that on a general hypersurface of degree r = 3, 4, 5, 6 in P 5 a rank 2 vector bundle E splits if and only if h 1 E(n) = h 2 E(n) = 0 for all n ∈ Z. Similar results for r = 1, 2 were obtained in [15], [16] and [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)

In this article we apply the classical method of focal loci of families to give a lower bound for the genus of curves lying on general surfaces. First we translate and reprove Xu's result that any curve C on a general surface in IP 3 of degree d ≥ 5 has geometric genus g > 1 + degC(d − 5)/2. Then we prove a similar lower bound for the curves lying on a… (More)

- L Chiantini, M Coppens
- 2000

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)

- L Chiantini, C Ciliberto
- 1999

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)