  This paper is concerned with the study of geometric structures in spaces of
polynomials. More precisely, we discuss for $E$ and $F$ Banach spaces, whether
the class of weakly continuous on bounded sets $n$-homogeneous polynomials,
$\mathcal P_w(^n E, F)$, is an HB-subspace or an $M(1,C)$-ideal in the space of
continuous $n$-homogeneous polynomials, $\mathcal P(^n E, F)$. We establish
sufficient conditions under which the problem can be positively solved. Some
examples are given. We also study when some ideal structures pass from
$\mathcal P_w(^n E, F)$ as an ideal in $\mathcal P(^n E, F)$ to the range space
$F$ as an ideal in its bidual $F^{**}$.
