David Eklund

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20092020

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math.AG2020

Sampling and homology via bottlenecks

Sandra Di Rocco, David Eklund, Oliver Gäfvert

In this paper we present an efficient algorithm to produce a provably dense sample of a smooth compact variety. The procedure is partly based on computing $bottlenecks$ of…

math.AG2019

The bottleneck degree of algebraic varieties

Sandra Di Rocco, David Eklund, Madeleine Weinstein

A bottleneck of a smooth algebraic variety $X \subset C^{n}$ is a pair of distinct points $(x, y) \in X$ such that the Euclidean normal spaces at $x$ and $y$ contain the line…

math.AG2018

The numerical algebraic geometry of bottlenecks

David Eklund

This is a computational study of bottlenecks on algebraic varieties. The bottlenecks of a smooth variety $X \subseteq C^{n}$ are the lines in $C^{n}$ which are normal…

math.AG2017

Numerical Polar calculus and cohomology of line bundles

Sandra Di Rocco, David Eklund, Chris Peterson

Let $L_{1}, \dots, L_{s}$ be line bundles on a smooth variety $X \subset P^{r}$ and let $D_{1}, \dots, D_{s}$ be divisors on $X$ such that $D_{i}$ represents $L_{i}$ . We give a probabilistic…

math.AG2009

Chern Numbers of Smooth Varieties via Homotopy Continuation and Intersection Theory

Sandra Di Rocco, David Eklund, Chris Petersen +1

Homotopy continuation provides a numerical tool for computing the equivalence of a smooth variety in an intersection product. Intersection theory provides a theoretical tool for re…