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In the present paper we construct two new explicit complex bordisms betweenany two projective bundles over $\mathbb{C} P^1$ of the same complex dimension,including the Milnor hypersurface $H_{1,n}$ and $\mathbb{C} P^1\times\mathbb{C} P^{n-1}$. These constructions reduce the bordism problem to thenull-bordism of some projective bundle over $\mathbb{C} P^1$ with thenon-standard stably complex structure.

The explicit geometric constructions of bordism of Milnor hypersurface $H_{1,n}$ and $\mathbb{C} P^1\times \mathbb{C} P^{n-1}$