Géométrie orthogonale non symétrique et congruences quadratiques

Jean-Marc Drézet (1)

1 IMJ - Institut de Mathématiques de Jussieu

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 $\P_1\times\P_1$.

Mots clés: congruences quadratiques; fibrés exceptionnels

Domaines: Géométrie algébrique [math.AG]

Jean-Marc Drézet. Géométrie orthogonale non symétrique et congruences quadratiques. Geometriae Dedicata, 2001, 86, pp.93-128. ⟨10.1023/A:1011992825774⟩. ⟨hal-00742455⟩