Ludvig Modin

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math.AG2026

Generalizations of Igusa surfaces

Pascal Fong, Matilde Maccan, Ludvig Modin

We give a criterion for the contracted product $E \times^{G} X$ to have a singular Picard scheme, where $E$ is an elliptic curve, $G \subset E$ is a finite subgroup scheme, and $X$ i…

math.AG2026

Intrinsic Non-Reductive Geometric Invariant Theory and Moduli Spaces of Principal Bundles with Non-Reductive Structure Groups

George Cooper, Ludvig Modin

We prove the existence of moduli spaces for algebraic stacks with a weak action of $Θ = [A^{1} / G_{m}]$ (including stacks of filtered objects and unstable $Θ$ -strata) f…

math.AG2026

Fundamental groups of proper algebraic stacks are finitely presented

Chirantan Chowdhury, Ludvig Modin

Lara, Srinivas and Stix showed that the étale fundamental group of a proper scheme over an algebraically closed field is topologically finitely presented. Building on this, we show…

math.AG2026

Obstructions to the existence of good moduli spaces of $A_{r}$ -stable curves

Davide Gori, Ludvig Modin, Michele Pernice

We study obstructions to the existence of separated good moduli spaces for open substacks of the moduli stack $M_{g, n}^{r}$ of $A_{r}$ -stable curves. Our approach is based on…

math.AG2026

The local geometry of the stack of $A_{r}$ -stable curves

Davide Gori, Ludvig Modin, Michele Pernice

In this paper we study the local geometry of the stack of pointed $A_{r}$ -stable curves. In particular, we analyze the deformation theory of $A_{r}$ -stable curves and their automorphis…

math.AG2025

Moduli spaces for $Θ$ -strata and non-reductive quotients

Ludvig Modin

We give a new proof of the $U^$ -theorem of Bérczi, Doran, Hawes and Kirwan on the existence of geometric quotients for actions of graded unipotent groups in terms of stacks of…

Generalizations of Igusa surfaces

Intrinsic Non-Reductive Geometric Invariant Theory and Moduli Spaces of Principal Bundles with Non-Reductive Structure Groups

Fundamental groups of proper algebraic stacks are finitely presented

Obstructions to the existence of good moduli spaces of Ar​-stable curves

The local geometry of the stack of Ar​-stable curves

Moduli spaces for Θ-strata and non-reductive quotients

Obstructions to the existence of good moduli spaces of $A_{r}$ -stable curves

The local geometry of the stack of $A_{r}$ -stable curves

Moduli spaces for $Θ$ -strata and non-reductive quotients