C. Peterson

activity

19972026

most citedPersistence Images: A Stable Vector Representation of Persistent Homology

172 citations · 305 across the 36 of their papers we have counts for

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Showing math.AGShow all

9 papers · 1 filter

math.AG2018★ 1 cited

On the Weak Lefschetz Property for Vector Bundles on $P^{2}$

Gioia Failla, Zachary Flores, Chris Peterson

Let $R = K [x, y, z]$ be a standard graded polynomial ring where $K$ is an algebraically closed field of characteristic zero. Let $M = \oplus_{j} M_{j}$ be a finite length g…

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.AG2016

Random fields and the enumerative geometry of lines on real and complex hypersurfaces

Saugata Basu, Antonio Lerario, Erik Lundberg +1

We derive a formula expressing the average number $E_{n}$ of real lines on a random hypersurface of degree $2 n - 3$ in $R P^{n}$ in terms of the expected modulus of the…

math.AG2015★ 9 cited

Eigenschemes and the Jordan canonical form

Hirotachi Abo, David Eklund, Thomas Kahle +1

We study the eigenscheme of a matrix which encodes information about the eigenvectors and generalized eigenvectors of a square matrix. The two main results in this paper are this d…

math.AG2011★ 17 cited

A method to compute Segre classes of subschemes of projective space

David Eklund, Christine Jost, Chris Peterson

We present a method to compute the degrees of the Segre classes of a subscheme of complex projective space. The method is based on generic residuation and intersection theory. It h…

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…

math.AG2009★ 5 cited

Non-Defectivity of Grassmannians of planes

Hirotachi Abo, Giorgio Ottaviani, Chris Peterson

Let $G r (k, n)$ be the Plücker embedding of the Grassmann variety of projective $k$ -planes in $¶ n$ . For a projective variety $X$ , let $σ_{s} (X)$ denote the variety of its $s - 1$ secant…

math.AG2006★ 4 cited

Induction for secant varieties of Segre varieties

Hirotachi Abo, Giorgio Ottaviani, Chris Peterson

This paper studies the dimension of secant varieties to Segre varieties. The problem is cast both in the setting of tensor algebra and in the setting of algebraic geometry. An indu…

math.AG2006

Implementation of Kumar's correspondence

Hirotachi Abo, Chris Peterson

In 1997, N.M. Kumar published a paper which introduced a new tool of use in the construction of algebraic vector bundles. Given a vector bundle on projective n-space, a well known…

On the Weak Lefschetz Property for Vector Bundles on P2