Emilia Mezzetti

Congruences of lines in \({{\mathbb P}^5}\), quadratic normality, and completely exceptional Monge–Ampère equations

The existence is proved of two new families of sextic threefolds in

On Threefolds Covered by Lines

{{\mathbb P}^5}

Togliatti systems and Galois coverings

, which are not quadratically normal. These threefolds arise naturally in the realm of first order congruences of lines as focal loci and in the study of the completely exceptional Monge–Ampère equations. One of these families comes from a smooth congruence of multidegree (1, 3, 3) which is a smooth Fano fourfold of index two and genus 9.

Smooth non-special surfaces of ℙ4

AbstractWe study the degeneracy loci of general bundle morphisms of the form

On the coefficients of the permanent and the determinant of a circulant matrix. Applications

\mathcal{O}

La sezione aurea, la spirale logaritmica e i numeri di Fibonacci

⊕mIPn → ΩIPn(2), also from the point of view of the classical geometrical interpretation of the sections of ΩIPn(2) as linear line complexes in IPn. We consider in particular the case of IP5 with m = 2, 3. For n = 5 and m = 3 we give an explicit description of the Hilbert scheme