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Let $M^{2n}$ be a unitary torus $(2n)$-manifold, i.e., a $(2n)$-dimensionaloriented stable complex connected closed $T^n$-manifold having a nonempty fixedset. In this paper we show that $M$ bounds equivariantly if and only if theequivariant Chern numbers $< (c_1^{T^n})^i(c_2^{T^n})^j, [M]>=0$ for all $i,j\in {\Bbb N}$, where $c_l^{T^n}$ denotes the $l$th equivariant Chern class of$M$. As a consequence, we also show that if $M$ does not bound equivariantlythen the number of fixed points is at least $\lceil{n\over2}\rceil+1$.

Equivariant Chern numbers and the number of fixed points for unitary torus manifolds