Non-vanishing theorems for rank two vector bundles on threefolds

The paper investigates the non-vanishing of $H^1(E(n))$, where $E$ is a (normalized) rank two vector bundle over any smooth irreducible threefold $X$ of degree $d$ such that Pic(X) \cong \ZZ. If $\epsilon$ is the integer defined by the equality $\omega_X = O_X(\epsilon)$, and $\alpha$ is the least integer $t$ such that $H^0(E(t)) \ne 0$, then, for a non-stable $E$ ($\alpha \le 0$) the first cohomology module does not vanish at least between the endpoints $\frac{\epsilon-c_1}{2}$ and $-\alpha-c_1-1$. The paper also shows that there are other non-vanishing intervals, whose endpoints depend on $\alpha$ and also on the second Chern class $c_2$ of $E$. If $E$ is stable the first cohomology module does not vanish at least between the endpoints $\frac{\epsilon-c_1}{2}$ and $\alpha-2$. The paper considers also the case of a threefold $X$ with Pic(X) \ne \ZZ but Num(X) \cong \ZZ and gives similar non-vanishing results.Comment: 18 page

On Buchsbaum bundles on quadric hypersurfaces

Let $E$ be an indecomposable rank two vector bundle on the projective space \PP^n, n \ge 3, over an algebraically closed field of characteristic zero. It is well known that $E$ is arithmetically Buchsbaum if and only if $n=3$ and $E$ is a null-correlation bundle. In the present paper we establish an analogous result for rank two indecomposable arithmetically Buchsbaum vector bundles on the smooth quadric hypersurface Q_n\subset\PP^{n+1}, $n\ge 3$. We give in fact a full classification and prove that $n$ must be at most 5. As to $k$-Buchsbaum rank two vector bundles on $Q_3$, $k\ge2$, we prove two boundedness results.Comment: 22 pages, no figur

La tutela cautelare

Il capitolo procede all'approfondimento della tutela cautelare disciplinata, all'interno del processo tributario, dall'art. 47 del d. lgs. 546/92. In primo luogo si dà spazio al profilo temporale, verificando che l'operatività dell'istituto non è molto risalente in tale processo, benché sia stata di recente estesa anche ai gradi di giudizio successivi al primo. Poi si procede ad una ampia trattazione dei requisiti richiesti dalla norma, ossia il fumus boni iuris ed il periculum in mora, accompagnata da una corposa ricerca giurisprudenziale sul punto. Successivamente si affrontano i temi attinenti alla procedura vera e propria. Infine, nell'ultima parte, si chiude con un cenno sul successivo art. 47-bis, ovvero sulla previsione di sospensiva in relazione alla procedura di recupero degli aiuti di Stato