On the distribution of ramification points in trigonal curves.
On the enumerative geometry of real algebraic curves having many real branches.
On the existence of k-normal curves of given degree and genus in projective spaces.
We find some ranges for the 4-tuples of integers (d,g,n,r) for which there is a smooth connected non-degenerate curve of degree d and genus g, which is k-normal for every k ≤ r.
On the Gauss maps of space curves in characteristic p, II
On the gonality of curves in
Here we study the gonality of several projective curves which arise in a natural way (e.gċurves with maximal genus in , curves with given degree and genus for all possible , if and with large for arbitrary ).
On the graded Betti numbers of plane algebraic curves.
On the Hilbert Scheme of Curves in Higher-dimensional Projective Space.
On the inseparable degrees of the Gauss map and the projection of the conormal variety to the dual fo higher order for space curves.
On the necessity of Reidemeister move 2 for simplifying immersed planar curves
In 2001, motivated by his results on finite-type knot diagram invariants, Östlund conjectured that Reidemeister moves 1 and 3 are sufficient to describe a homotopy from any generic immersion S¹ → ℝ² to the standard embedding of the circle. We show that this conjecture is false.
On the real X -ranks of points of P n (R) with respect to a real variety X ⊂ P n
Let X ⊂ Pn be an integral and non-degenerate m-dimensional variety defined over R. For any P ∈ Pn(R) the real X-rank r x,R(P) is the minimal cardinality of S ⊂ X(R) such that P ∈ . Here we extend to the real case an upper bound for the X-rank due to Landsberg and Teitler.
On the smallest degree of a surface containing a space curve
Sia una curva dello spazio di grado contenuta in una superficie di grado e non in una di grado . Se è integra, allora ; questo limite superiore, raggiunto in alcuni casi (cfr. [5]), non vale però per curve arbitrarie (cfr. [?, 3 (iii)]). Ogni curva dello spazio (anche non ridotta o riducibile) può essere ottenuta come schema degli zero di una sezione non nulla di un opportuno fascio riflessivo di rango 2. Mediante i fasci riflessivi, siamo in grado di estendere alle curve riducibili...
On the space curves with the same dual varietey.
On the space curves with the same image under the Gauss maps.
On the stability of the restricted bundle of space curves contained in a quartic surface.
On vanishing inflection points of plane curves
We study the local behaviour of inflection points of families of plane curves in the projective plane. We develop normal forms and versal deformation concepts for holomorphic function germs which take into account the inflection points of the fibres of . We give a classification of such function- germs which is a projective analog of Arnold’s A,D,E classification. We compute the versal deformation with respect to inflections of Morse function-germs.
Orbifold principal bundles on an elliptic fibration and parabolic principal bundles on a Riemann surface.
Let X be a compact Riemann surface and associated to each point p-i of a finite subset S of X is a positive integer m-i. Fix an elliptic curve C. To this data we associate a smooth elliptic surface Z fibered over X. The group C acts on Z with X as the quotient. It is shown that the space of all vector bundles over Z equipped with a lift of the action of C is in bijective correspondence with the space of all parabolic bundles over X with parabolic structure over S and the parabolic weights at any...
Order of torsion in of quadrics.