MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Sampling from the uniform distribution on an algebraic manifold

Paul Breiding and Orlando Marigliano


Let $\mathcal M$ be an open submanifold of an affine algebraic variety. We can pick a point from $\mathcal M$ by first choosing an affine-linear space $\mathcal L$ of complementary dimension and then choosing one of the intersection points $x$. We propose distributions on the set of linear spaces $\mathcal L$ and on the sets $\mathcal M \cap \mathcal L$ 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.


Related publications

2020 Repository Open Access
Paul Breiding and Orlando Marigliano

Random points on an algebraic manifold

In: SIAM journal on mathematics of data science, 2 (2020) 3, pp. 683-704