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Geometrical properties of the lifting-up technique in support vector machines (SVMs) are discussed here. In many applications, an SVM finds the optimal inhomogeneous separating hyperplane in terms of margins while some of the theoretical analyses on SVMs have treated only homogeneous hyperplanes for simplicity. Although they seem equivalent due to the so-called lifting-up technique, they differ in fact and the solution of the homogeneous SVM with lifting-up strongly depends on the parameter of lifting-up. It is also shown that the solution approaches that of the inhomogeneous SVM in the asymptotic case that the parameter goes to infinity.