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Non-special projectively normal line bundles on general k-gonal curves

100%
Ballico E.
Annales Polonici Mathematici
|
2004
|
tom 84
|
nr 1
55-60
EN
Let X be a sufficiently general smooth k-gonal curve of genus g and R ∈ Pic(X) the degree k spanned line bundle. We find an optimal integer z > 0 such that the line bundle $R^{⊗z}$ is very ample and projectively normal.
2
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On the birational gonalities of smooth curves

100%
Ballico E.
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
|
2014
|
tom 68
|
nr 1
EN
Let \(C\) be a smooth curve of genus \(g\). For each positive integer \(r\) the birational \(r\)-gonality \(s_r(C)\) of \(C\) is the minimal integer \(t\) such that there is \(L\in \mbox{Pic}^t(C)\) with \(h^0(C,L) =r+1\). Fix an integer \(r\ge 3\). In this paper we prove the existence of an integer \(g_r\) such that for every integer \(g\ge g_r\) there is a smooth curve \(C\) of genus \(g\) with \(s_{r+1}(C)/(r+1) > s_r(C)/r\), i.e. in the sequence of all birational gonalities of \(C\) at least one of the slope inequalities fails.
3
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On the graded Betti numbers for large finite subsets of curves

100%
Ballico E.
Annales Polonici Mathematici
|
1998
|
tom 69
|
nr 3
283-286
EN
We prove a recent conjecture of S. Lvovski concerning the periodicity behaviour of top Betti numbers of general finite subsets with large cardinality of an irreducible curve C ⊂ ℙⁿ.
4
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On the secant varieties to the osculating variety of a Veronese surface

64%
Ballico E., Fontanari C.
Open Mathematics
|
2003
|
tom 1
|
nr 3
315-326
EN
In this paper we study the k-th osculating variety of the order d Veronese embedding of P n. In particular, for k=n=2 we show that the corresponding secant varieties have the expected dimension except in one case.
5
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On the Hilbert function of curvilinear zero-dimensional subschemes of projective spaces

51%
Ballico E., Notari R., Spreafico M.
Open Mathematics
|
2003
|
tom 1
|
nr 4
644-649
EN
Here we show the existence of strong restrictions for the Hilbert function of zerodimensional curvilinear subschemes of P n with one point as support and with high regularity index.
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