Jeremy Usatine

activity

20122026

most citedThe motivic zeta functions of a matroid

9 citations · 22 across the 16 of their papers we have counts for

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Showing math.AGShow all

13 papers · 1 filter

math.AG2026

McKay correspondence for linearly reductive finite group schemes in positive characteristic

Matthew Satriano, Jeremy Usatine

We obtain a motivic and a cohomological McKay correspondence for finite linearly reductive group schemes in arbitrary characteristic. In particular, we prove that if $V$ is a finit…

math.AG2026

A counter-example to Batyrev's conjecture on the non-negativity of stringy Hodge numbers

Matthew Satriano, Jeremy Usatine

Batyrev's conjecture on the non-negativity of stringy Hodge numbers has been a fundamental open problem, guiding and motivating many beautiful mathematical results in motivic integ…

math.AG2026

A cohomological interpretation for stringy Hodge numbers

Jiahui Huang, Matthew Satriano, Jeremy Usatine

We obtain a cohomological interpretation for Batyrev's stringy Hodge numbers in the full generality in which they are defined. In a previous paper, the second and third authors use…

math.AG2024

Stringy Hodge numbers via crepant resolutions by Artin stacks

Matthew Satriano, Jeremy Usatine

In a previous paper we showed that any variety with log-terminal singularities admits a crepant resolution by a smooth Artin stack. In this paper we prove the converse, thereby pro…

math.AG2023

Motivic integration for singular Artin stacks

Matthew Satriano, Jeremy Usatine

Let $X \to Y$ be a birational modification of a variety by an Artin stack. In previous work, under the assumption that $X$ is smooth, we proved a change of vari…

math.AG2023

Beyond twisted arcs: a McKay correspondence for reductive groups

Matthew Satriano, Jeremy Usatine

We introduce a natural generalization of twisted maps, called \emph{warped maps}. While twisted maps play an important role in the study of Deligne--Mumford stacks, warped maps are…

math.AG2023

Crepant resolutions of log-terminal singularities via Artin stacks

Matthew Satriano, Jeremy Usatine

We prove that every variety with log-terminal singularities admits a crepant resolution by a smooth Artin stack. We additionally prove new McKay correspondences for resolutions by…

math.AG2021★ 1 cited

A motivic change of variables formula for Artin stacks

Matthew Satriano, Jeremy Usatine

Let $X \to Y$ be a birational map from a smooth Artin stack to a (possibly singular) variety. We prove a change of variables formula that relates motivic integrals over a…

math.AG2021

Gromov-Witten theory and invariants of matroids

Dhruv Ranganathan, Jeremy Usatine

We use techniques from Gromov-Witten theory to construct new invariants of matroids taking value in the Chow groups of spaces of rational curves in the permutohedral toric variety.…

math.AG2020★ 4 cited

Stringy invariants and toric Artin stacks

Matthew Satriano, Jeremy Usatine

We propose a conjectural framework for computing Gorenstein measures and stringy Hodge numbers in terms of motivic integration over arcs of smooth Artin stacks, and we verify this…

math.AG2018

Motivic zeta functions of hyperplane arrangements

Max Kutler, Jeremy Usatine

For each central essential hyperplane arrangement $A$ over an algebraically closed field, let $Z_{A}^{μ^} (T)$ denote the Denef-Loeser motivic zeta function of…

math.AG2018

Hyperplane arrangements and mixed Hodge numbers of the Milnor fiber

Max Kutler, Jeremy Usatine

For each complex central essential hyperplane arrangement $A$ , let $F_{A}$ denote its Milnor fiber. We use Tevelev's theory of tropical compactifications to stu…

math.AG2018

Motivic Volumes of Fibers of Tropicalization

Jeremy Usatine

Let $T$ be an algebraic torus over an algebraically closed field, let $X$ be a smooth closed subvariety of a $T$ -toric variety such that $U = X \cap T$ is not empty, and let $\math…