## Trois nouveaux théorèmes sur les systèmes linéaires de quadriques à Jacobienne identiquement nulle.(French)Zbl 0542.14033

This note is devoted to give a characterization of d-dimensional linear systems of quadrics in $${\mathbb{P}}^ r$$, with Jacobian matrix of rank r- $$k\leq d$$ and $$d\leq r$$. The author divides such systems in two types: the irreducible and the reducible ones. For the first ones the characterization is as follows: the quadrics of the system passing through a general point of $${\mathbb{P}}^ r$$ have a $${\mathbb{P}}^{k+1}$$ in common. An analogous property holds for reducible systems. Though it is never stated explicitly, the base field has to be assumed of characteristic zero.
It seems to the reviewer the exposition is unfortunately rather obscure.
Reviewer: C.Ciliberto

### MSC:

 14N05 Projective techniques in algebraic geometry 51N15 Projective analytic geometry 14C20 Divisors, linear systems, invertible sheaves

### Keywords:

$$d$$-dimensional linear systems of quadrics
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