Robert Silversmith

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20162021

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math.AG2021

Cross-ratio degrees and perfect matchings

Rob Silversmith

Cross-ratio degrees count configurations of points $z_{1}, \dots, z_{n} \in P^{1}$ satisfying $n - 3$ cross-ratio constraints, up to isomorphism. These numbers arise in multiple…

math.AG2020

Equations at infinity for critical-orbit-relation families of rational maps

Rohini Ramadas, Rob Silversmith

We develop techniques for using compactifications of Hurwitz spaces to study families of rational maps $P^{1} \to P^{1}$ defined by critical orbit relations. We apply t…

math.AG2020

Two-dimensional cycle classes on $M_{0, n}$

Rohini Ramadas, Rob Silversmith

For each $n \geq 5$ , we give an $S_{n}$ -equivariant basis for $H_{4} (M_{0, n}, Q)$ , as well as for $H_{2 (n - 5)} (M_{0, n}, Q)$ . Such…

math.AG2019

The matroid stratification of the Hilbert scheme of points on P^1

Rob Silversmith

Given a homogeneous ideal $I$ in a polynomial ring over a field, one may record, for each degree $d$ and for each polynomial $f \in I_{d}$ , the set of monomials in $f$ with nonzero co…

math.AG2016

Gromov-Witten theory of toroidal orbifolds and GIT wall-crossing