  We study ideals which are generated by monomials of degree $d$ in the
polynomial ring in $n$ variables and which satisfy certain numerical side
conditions regarding their exponents. Typical examples of such ideals are the
ideals of Veronese type, squarefree Veronese ideals or $t$-spread Veronese
ideals. In this paper we focus on $c$-bounded $t$-spread Veronese ideals and on
Veronese ideals of bounded support. Their powers as well as their fiber cone is
also be considered.
