  The aim of this paper is to give a higher dimensional equivalent of the
classical modular polynomials $\Phi_\ell(X,Y)$. If $j$ is the $j$-invariant
associated to an elliptic curve $E_k$ over a field $k$ then the roots of
$\Phi_\ell(j,X)$ correspond to the $j$-invariants of the curves which are
$\ell$-isogeneous to $E_k$. Denote by $X_0(N)$ the modular curve which
parametrizes the set of elliptic curves together with a $N$-torsion subgroup.
It is possible to interpret $\Phi_\ell(X,Y)$ as an equation cutting out the
image of a certain modular correspondence $X_0(\ell) \to X_0(1) \times X_0(1)$
in the product $X_0(1) \times X_0(1)$. Let $g$ be a positive integer and
$\overn \in \N^g$. We are interested in the moduli space that we denote by
$\Mn$ of abelian varieties of dimension $g$ over a field $k$ together with an
ample symmetric line bundle $\pol$ and a symmetric theta structure of type
$\overn$. If $\ell$ is a prime and let $\overl=(\ell, ..., \ell)$, there exists
a modular correspondence $\Mln \to \Mn \times \Mn$. We give a system of
algebraic equations defining the image of this modular correspondence.
