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- Luca Chiantini, E Sernesi
- 1996

the family Vd,δ of plane irreducible curves of degree d having exactly δ nodes and no other singularities is non empty and everywhere smooth of codimension δ in the linear system |O(d)|. If C ∈ Vd,δ Severi uses the non speciality of the normal line bundle to the composition ν : C̃ → C → P, where C̃ is the normalization of C, to prove that Vd,δ is smooth of… (More)

- Luca Chiantini, CARLO MADONNA
- 2004

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

For an irreducible projective variety X, we study the family of h-planes contained in the secant variety Seck(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 expected… (More)

- Luca Chiantini, Giorgio Ottaviani
- SIAM J. Matrix Analysis Applications
- 2012

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 P3 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)

- 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 every arithmetically Cohen–Macaulay rank 2 vector bundle is infinitesimally rigid.

- Luca Chiantini, C . MADONNA
- 2004

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

A linear series g δ on a curve C ⊂ P 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 : hIC(i) 6= 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)

- Luca Chiantini, Giorgio Ottaviani, Nick Vannieuwenhoven
- SIAM J. Matrix Analysis Applications
- 2014