Johannes Schmitt

activity

20162026

most citedadmcycles -- a Sage package for calculations in the tautological ring of the moduli space of stable curves

50 citations · 108 across the 18 of their papers we have counts for

collaborators

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19 papers · 1 filter

math.AG2026

Euler characteristics of strata of $k$ -differentials

Matteo Costantini, Alessandro Giacchetto, Martin Möller +2

We compute the orbifold Euler characteristics of strata of $k$ -differentials on the moduli space of smooth pointed curves. Our main result is a closed coefficient-extraction formul…

math.AG2024

$k$ -leaky double Hurwitz descendants

Renzo Cavalieri, Hannah Markwig, Johannes Schmitt

We define a new class of enumerative invariants called $k$ -leaky double Hurwitz descendants, generalizing both descendant integrals of double ramification cycles and the $k$ -leaky…

math.AG2023

Birational classification of toric orbifolds

Johannes Schmitt

We give a complete classification of the torus-equivariant birational equivalence classes of smooth proper toric Deligne-Mumford stacks with trivial generic stabilizer in terms of…

math.AG2022★ 1 cited

A tale of two moduli spaces: logarithmic and multi-scale differentials

Dawei Chen, Samuel Grushevsky, David Holmes +2

Multi-scale differentials were constructed by M.~Bainbridge, D.~Chen, Q.~Gendron, S.~Grushevsky, and M.~Möller, from the viewpoint of flat and complex geometry, for the purpose of…

math.AG2022

Étale cohomological stability of the moduli space of stable elliptic surfaces

Oishee Banerjee, Jun-Yong Park, Johannes Schmitt

We compute the (stable) étale cohomology of $Hom_{n} (C, P (λ))$ , the moduli stack of degree $n$ morphisms from a smooth projective curve $C$ to the weighted p…

math.AG2022★ 5 cited

Logarithmic double ramification cycles

D. Holmes, S. Molcho, R. Pandharipande +2

Let $A = (a_{1}, \dots, a_{n})$ be a vector of integers which sum to $k (2 g - 2 + n)$ . The double ramification cycle $DR_{g, A} \in CH^{g} (M_{g, n})$ on the moduli spac…

math.AG2021★ 2 cited

Integrals of $ψ$ -classes on twisted double ramification cycles and spaces of differentials

Matteo Costantini, Adrien Sauvaget, Johannes Schmitt

We prove a closed formula for the integral of a power of a single $ψ$ -class on strata of $k$ -differentials. In many cases, these integrals correspond to intersection numbers on twi…

math.AG2021

Chow rings of stacks of prestable curves II

Younghan Bae, Johannes Schmitt

We continue the study of the Chow ring of the moduli stack $M_{g, n}$ of prestable curves begun in [arXiv:2012.09887v2]. In genus $0$ , we show that the Chow ring of $\mat…

math.AG2021★ 3 cited

The Hodge bundle, the universal 0-section, and the log Chow ring of the moduli space of curves

Samouil Molcho, Rahul Pandharipande, Johannes Schmitt

We bound from below the complexity of the top Chern class of the Hodge bundle in the Chow ring of the moduli space of curves: no formulas in terms of classes of degrees 1 and 2 can…

math.AG2020★ 19 cited

Chow rings of stacks of prestable curves I

Younghan Bae, Johannes Schmitt

We study the Chow ring of the moduli stack $M_{g, n}$ of prestable curves and define the notion of tautological classes on this stack. We extend formulas for intersection…

math.AG2020★ 9 cited

Pixton's formula and Abel-Jacobi theory on the Picard stack

Younghan Bae, David Holmes, Rahul Pandharipande +2

Let $A = (a_{1}, \dots, a_{n})$ be a vector of integers with $d = \sum_{i = 1}^{n} a_{i}$ . By partial resolution of the classical Abel-Jacobi map, we construct a universal twisted double ramifica…

math.AG2020★ 50 cited

admcycles -- a Sage package for calculations in the tautological ring of the moduli space of stable curves

Vincent Delecroix, Johannes Schmitt, Jason van Zelm

The tautological ring of the moduli space of stable curves has been studied extensively in the last decades. We present a SageMath implementation of many core features of this ring…

math.AG2019★ 13 cited

Infinitesimal structure of the pluricanonical double ramification locus

David Holmes, Johannes Schmitt

We prove that a formula for the `pluricanonical' double ramification cycle proposed by Janda, Pandharipande, Pixton, Zvonkine, and the second-named author is in fact the class of a…

math.AG2019★ 4 cited

Zero cycles on the moduli space of curves

Rahul Pandharipande, Johannes Schmitt

While the Chow groups of 0-dimensional cycles on the moduli spaces of Deligne-Mumford stable pointed curves can be very complicated, the span of the 0-dimensional tautological cycl…

math.AG2018

Intersections of loci of admissible covers with tautological classes

Johannes Schmitt, Jason van Zelm

For a finite group $G$ , let $\H_{g,G,ξ}$ be the stack of admissible $G$ -covers $C \to D$ of stable curves with ramification data $ξ$ , $g (C) = g$ and $g (D) = g^{'}$ . There are source and ta…

math.AG2017

Multiplicativity of the double ramification cycle

David Holmes, Aaron Pixton, Johannes Schmitt

The double ramification cycle satisfies a basic multiplicative relation DRC(a).DRC(b) = DRC(a).DRC(a + b) over the locus of compact-type curves, but this relation fails in the Chow…

math.AG2016

A correspondence of good G-sets under partial geometric quotients

Johannes Schmitt

For a complex variety $X^$ with an action of a reductive group $G^$ and a geometric quotient $π : X^\to X$ by a closed normal subgroup $H \subset G^$ , we show that…

math.AG2016

Dimension theory of the moduli space of twisted $k$ -differentials

Johannes Schmitt

In this note we extend the dimension theory for the spaces $H_{g}^{k} (μ)$ of twisted $k$ -differentials defined by Farkas and Pandharipande in [FP15] to the case $k…

math.AG2016

A compactification of the moduli space of self-maps of $CP^{1}$ using stable maps

Johannes Schmitt

We present a new compactification $M (d, n)$ of the moduli space of self-maps of $CP^{1}$ of degree $d$ with $n$ markings. It is constructed via GIT from the stable maps modul…

Euler characteristics of strata of k-differentials

k-leaky double Hurwitz descendants

Birational classification of toric orbifolds

A tale of two moduli spaces: logarithmic and multi-scale differentials

Étale cohomological stability of the moduli space of stable elliptic surfaces

Logarithmic double ramification cycles

Integrals of ψ-classes on twisted double ramification cycles and spaces of differentials

Chow rings of stacks of prestable curves II

The Hodge bundle, the universal 0-section, and the log Chow ring of the moduli space of curves

Chow rings of stacks of prestable curves I

Pixton's formula and Abel-Jacobi theory on the Picard stack

admcycles -- a Sage package for calculations in the tautological ring of the moduli space of stable curves

Infinitesimal structure of the pluricanonical double ramification locus

Zero cycles on the moduli space of curves

Intersections of loci of admissible covers with tautological classes

Multiplicativity of the double ramification cycle

A correspondence of good G-sets under partial geometric quotients

Dimension theory of the moduli space of twisted k-differentials

A compactification of the moduli space of self-maps of CP1 using stable maps

Euler characteristics of strata of $k$ -differentials

$k$ -leaky double Hurwitz descendants

Integrals of $ψ$ -classes on twisted double ramification cycles and spaces of differentials

Dimension theory of the moduli space of twisted $k$ -differentials

A compactification of the moduli space of self-maps of $CP^{1}$ using stable maps