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

Offset Hypersurfaces and Persistent Homology of Algebraic Varieties

Madeleine Weinstein and Emil Horobet


In this paper, we study the true persistent homology of algebraic varieties. We prove the algebraicity of two quantities central to the computation of persistent homology. Moreover, we connect persistent homology and algebraic optimization (Euclidean Distance Degree). Namely, we express the degree corresponding to the distance variable of the offset hypersurface in terms of the Euclidean Distance degree of the starting variety, obtaining a new way to compute these degrees. Finally, we describe the non-properness locus of the offset construction and use this to describe the set of points that are topologically interesting (the medial axis and center points of the bounded components of the complement of the variety) and relevant to the computation of persistent homology.


Related publications

2019 Repository Open Access
Emil Horobet and Madeleine Weinstein

Offset hypersurfaces and persistent homology of algebraic varieties

In: Computer aided geometric design, 74 (2019), p. 101767