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 1 Introduction
The Milnor hypersurfaces, denoted , are a family of smooth manifolds that generate (with redundancy) the complex bordism ring.
 2 Construction and examples
For fixed natural numbers , is defined as the hypersurface in satisfying the equation , where and are homogeneous coordinates for and respectively. This equation defines a generic hyperplane intersecting the image of the Segre embedding transversely.
The role of these manifolds in complex bordism is described on the page Complex bordism.
 3 Invariants
The signature of the Milnor hypersurfaces is known: