Consider a complete intersection $X=Q_0 \cap Q_1$ of two quadrics in $\mathbb P^5.$ Choose a line $L\subset X$ and a $V_3 \equiv \mathbb P^3$ disjoint from $L.$ Consider the projection $\pi : \mathbb P^5 \longrightarrow M$ with center $L$ and restric $\pi$ to $X,$ this gives a birational map from $X$ to $M$ whose inverse is not defined at the genus two quintic in $M$ given by a quadric and two quartics. In a joint paper with I. Pan and G. Gonzalez Sprinberg we applied this to study the Cremona transformations that one obtains from this set up by considering two such projections by choosing two such lines. In this seminar I will explain this and talk about a joint work in progress with C. Peskine where we are trying to extend this construction by considering a linear system of quadrics in $\mathbb P^N$ containing a linear space. Time allowing I will consider an application of this to Fano varieties.