In this paper we prove that the projective dimension of ${ℳ}_n=R^4/⟨A_n⟩$ is $2n-1$, where $R$ is the ring of polynomials in $4n$ variables with complex coefficients, and $⟨A_n⟩$ is the module generated by the columns of a $4\times 4n$ matrix which arises as the Fourier transform of the matrix of differential operators associated with the regularity condition for a function of $n$ quaternionic variables. As a corollary we show that the sheaf $ℛ$ of regular functions has flabby dimension $2n-1$, and we prove a cohomology vanishing theorem for open...

We present bounds for the degree and the height of the polynomials arising in some problems in effective algebraic geometry including the implicitization of rational maps and the effective Nullstellensatz over a variety. Our treatment is based on arithmetic intersection theory in products of projective spaces and extends to the arithmetic setting constructions and results due to Jelonek. A key role is played by the notion of canonical mixed height of a multiprojective variety. We study this notion...

Lo scopo di questo lavoro è la descrizione di alcune nuove tecniche per calcolare serie di Hilbert-Poincaré (HP-serie) di algebre standard, che possono essere viste come sottoalgebre di algebre bigraduate. In particolare mostriamo come calcolare in modo uniforme le HP-serie delle potenze di un idele omogeneo. Mostriamo anche come calcolare le HP-serie di prodotti di Segre e di alcune algebre di Blow-up, che sono di interesse in Geometria Algebrica. Per alcune classi siamo in grado di descrivere...