On the principal bundles over a flag manifold.
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...
The structure of 3-folds in P6 which are generally linked via a complete intersection (f1,f2,f3) to 3-folds in P6 of degree d ≤ 5 is determined. We also give three new examples of smooth 3-folds in P6 of degree 11 and genus 9. These examples are obtained via liaison. The first two are 3-folds linked via a complete intersection (2,3,3) to 3-folds in P6 of degree 7: (i) the hyperquadric fibration over P1 and (ii) the scroll over P2. The third example is Pfaffian linked to a 3-dimensional quadric in...
In the current paper we show that the dimension of a family of irreducible reduced curves in a given ample linear system on a toric surface over an algebraically closed field is bounded from above by , where denotes a general curve in the family. This result generalizes a famous theorem of Zariski to the case of positive characteristic. We also explore new phenomena that occur in positive characteristic: We show that the equality does not imply the nodality of even if belongs to the...