Géométrie orthogonale non symétrique et congruences quadratiques. Geometriae Dedicata 86 (2001) , 93-128.

The subject of this paper is the study of quadratic congruences. Let $W\subset H^0(\P_n,{\mathcal O}(2))$ be a linear subspace of dimension n+1. A quadratic congruence is a rational morphism
$\sigma : \P_n\longrightarrow{\mathbb P}(W)$
such that $\sigma^*({\mathcal O}(1))\simeq{\mathcal O}(2)$$\sigma^*:W^*\longrightarrowH^0(\P_n,{\mathcal O}(2))$  induces an isomorphism $W^*\simeq W$,  and for each $x\in\P_n$, x belongs to the conic defined by $\sigma(x)$. Quadratic congruences appear in the theory of exceptional bundles on $\P_3$ and $\P_1\times\P_1$.

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