Sampling from the uniform distribution on an algebraic manifold

Paul Breiding and Orlando Marigliano

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Submission date: 17. Oct. 2018
Bibtex
Link to arXiv: See the arXiv entry of this preprint.

Abstract:
Let ℳ be an open submanifold of an affine algebraic variety. We can pick a point from ℳ by first choosing an affine-linear space ℒ of complementary dimension and then choosing one of the intersection points x. We propose distributions on the set of linear spaces ℒ and on the sets ℳ∩ℒ of intersection points such that the points x chosen with the procedure above are uniformly distributed. We do the same for the projective setting and demonstrate the proposed method in the context of topological data analysis.