Introduction to the hyperdeterminant and to the rank of multidimensional matrices

This is an introduction to the hyperderminant, according to Gelfand, Kapranov and Zelevinsky. The "triangle inequality", characterizing the Segre varieties such that their dual variety is a hypersurface, is proved in a geometric way (Theorems 3.3 and 6.2). Significant emphasis is given to boundary format case, to pencil of quadrics and to the rank of multidimensional matrices. In the last section we propose three open problems.Comment: 29 pages, 10 figures, expository pape

The Value of Public Information in Monopoly

The logic of the linkage principle of Milgrom and Weber (1982) extends to price discrimination. A non-linear pricing monopolist who sells to a single buyer always prefers to commit to publicly reveal information affiliated to the valuation of the buyer.

On singular Luroth quartics

Plane quartics containing the ten vertices of a complete pentalateral and limits of them are called L\"uroth quartics. The locus of singular L\"uroth quartics has two irreducible components, both of codimension two in $\P^{14}$. We compute the degree of them and we discuss the consequences of this computation on the explicit form of the L\"uroth invariant. One important tool are the Cremona hexahedral equations of the cubic surface. We also compute the class in $\overline{M}_3$ of the closure of the locus of nonsingular L\"uroth quartics.Comment: Enlarged version. Computation of the class of the locus of Luroth quartics in the moduli space adde