42 citations · 123 across the 18 of their papers we have counts for
23 papers
Joseph Carter Corbin: Arkansas's "Profound Mathematician''
Jesse Leo Kass
This is a historical article on J. C. Corbin, a nineteenth century mathematician and the founding president of the Historically Black University of Arkansas at Pine Bluff. This ver…
A relative orientation for the moduli space of stable maps to a del Pezzo surface
Jesse Leo Kass, Marc Levine, Jake P. Solomon +1
We prove orientation results for evaluation maps of moduli spaces of rational stable maps to del Pezzo surfaces over a field, both in characteristic and in positive characteris…
A quadratically enriched count of rational curves
Jesse Leo Kass, Marc Levine, Jake P. Solomon +1
We define a quadratically enriched count of rational curves in a given divisor class passing through a collection of points on a del Pezzo surface of degree over a per…
What is the height of two points in the plane?
Jesse Leo Kass, Frank Thorne
Here we describe the distribution of rational points on the Hilbert scheme of two points in the projective plane. More specifically, we explicitly describe a two-parameter family o…
An Example of Wild Ramification in an Enriched Riemann-Hurwitz Formula
Candace Bethea, Jesse Leo Kass, Kirsten Wickelgren
M. Levine proved an enrichment of the classical Riemann-Hurwitz formula to an equality in the Grothendieck-Witt group of quadratic forms. In its strongest form, Levine's theorem in…
Extending the Double Ramification Cycle using Jacobians
David Holmes, Jesse Leo Kass, Nicola Pagani
We prove that the extension of the double ramification cycle defined by the first-named author (using modifications of the stack of stable curves) coincides with that defined by th…
An étale realization which does not exist
Jesse Leo Kass, Kirsten Wickelgren
For a global field, local field, or finite field with infinite Galois group, we show that there can not exist a functor from the Morel--Voevodsky -homotopy catego…
The stability space of compactified universal Jacobians
Jesse Leo Kass, Nicola Pagani
In this paper we describe compactified universal Jacobians, i.e. compactifications of the moduli space of line bundles on smooth curves obtained as moduli spaces of rank 1 torsion-…
The class of Eisenbud--Khimshiashvili--Levine is the local A1-Brouwer degree
Jesse Leo Kass, Kirsten Wickelgren
Given a polynomial function with an isolated zero at the origin, we prove that the local A1-Brouwer degree equals the Eisenbud-Khimshiashvili-Levine class. This answers a question…
A classical proof that the algebraic homotopy class of a rational function is the residue pairing
Jesse Leo Kass, Kirsten Wickelgren
Cazanave has identified the algebraic homotopy class of a rational function of variable with an explicit nondegenerate symmetric bilinear form. Here we show that Hurwitz's proo…
Singular curves and their compactified Jacobians
Jesse Leo Kass
We survey the theory of the compactified Jacobian associated to a singular curve. We focus on describing low genus examples using the Abel map.
An explicit semi-factorial compactification of the Néron model
Jesse Leo Kass
C.~Pépin recently constructed a semi-factorial compactification of the Néron model of an abelian variety using the flattening technique of Raynaud--Gruson. Here we prove that an ex…
The compactified jacobian can be nonreduced
Jesse Leo Kass
We prove by explicit example that the compactified jacobian can be nonreduced. The example is a rational space curve of arithmetic genus 4. This answers a question posed by Cyril D…
Autoduality holds for a degenerating abelian variety
Jesse Leo Kass
We prove that certain degenerate abelian varieties, the compactified Jacobian of a nodal curve and a stable quasiabelian variety, satisfy autoduality. We establish this result by p…
Extensions of the universal theta divisor
Jesse Leo Kass, Nicola Pagani
The Jacobian varieties of smooth curves fit together to form a family, the universal Jacobian, over the moduli space of smooth marked curves, and the theta divisors of these curves…
The singularities and birational geometry of the universal compactified Jacobian
Sebastian Casalaina-Martin, Jesse Leo Kass, Filippo Viviani
In this paper we establish that the singularities of the universal compactified Jacobian are canonical if the genus is at least four. As a corollary we determine the Kodaira dimens…
An Abel map to the compactified Picard scheme realizes Poincaré duality
Jesse Leo Kass, Kirsten Wickelgren
For a smooth algebraic curve X over a field, applying H_1 to the Abel map X -> Pic (X/\partial X) to the Picard scheme of X modulo its boundary realizes the Poincaré duality isomor…
An Explicit Non-smoothable Component of the Compactified Jacobian
Jesse Leo Kass
This paper studies the components of the moduli space of rank 1, torsion-free sheaves, or compactified Jacobian, of a non-Gorenstein curve. We exhibit a generically reduced compone…
The Local Structure of Compactified Jacobians
Sebastian Casalaina-Martin, Jesse Leo Kass, Filippo Viviani
This paper studies the local geometry of compactified Jacobians constructed by Caporaso, Oda-Seshadri, Pandharipande, and Simpson. The main result is a presentation of the complete…
Moduli of Generalized Line Bundles on a Ribbon
Dawei Chen, Jesse Leo Kass
A ribbon is a first-order thickening of a non-singular curve. Motivated by a question of Eisenbud and Green, we show that a compactification of the moduli space of line bundles on…
The geometry and combinatorics of cographic toric face rings
Sebastian Casalaina-Martin, Jesse Leo Kass, Filippo Viviani
In this paper we define and study a ring associated to a graph that we call the cographic toric face ring, or simply the cographic ring. The cographic ring is the toric face ring d…
Two ways to degenerate the Jacobian are the same
Jesse Leo Kass
A basic technique for studying a family of Jacobian varieties is to extend the family by adding degenerate fibers. Constructing an extension requires a choice of fibers, and one ty…
A Riemann singularity theorem for integral curves
Sebastian Casalaina-Martin, Jesse Leo Kass
We prove results generalizing the classical Riemann Singularity Theorem to the case of integral, singular curves. The main result is a computation of the multiplicity of the theta…