4 problems

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Riemenschneider's conjecture on special representations of cyclic quotient singularities
Let $G$ be a finite small cyclic subgroup of $\operatorname{GL}(2,\mathbb{C})$ , and let $\operatorname{Hilb}^G(\mathbb{C}^2)$ be the $G$ -Hilbert scheme. The irreducible representat…
Conjectureopencyclic-quotient-singularities mckay-correspondence representation-theoryarXiv posted 2 days ago
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Mori–Morrison–Morrison classification conjecture for four-dimensional terminal cyclic quotient singularities
A four-dimensional terminal cyclic quotient singularity of prime index is classified through the notion of a series: a series is a closed subgroup $V\subset T^n$ , together with fin…
Conjecturesolvedcyclic-quotient-singularities singularity-classification toric-singularitiesarXiv posted 2 days ago
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Brohme-Stevens radical ideal conjecture for cyclic quotient deformation spaces
Let $J$ be the ideal of the base space of the versal deformation of a cyclic quotient singularity of embedding dimension $e$ , and let $\sqrt J$ be its radical. Let $J'$ be the idea…
Conjecturesolvedcyclic-quotient-singularities deformation-theory singularity-theoryarXiv posted 2 days ago
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Arndt's Catalan bound for components of cyclic quotient deformation spaces
Arndt's conjecture. The number of irreducible components of the versal deformation base space should not exceed $C_{e-3}$ . This conjecture was proved by Jan Stevens using Kollár an…
Conjecturesolvedcyclic-quotient-singularities deformation-theory singularity-theoryarXiv posted 2 days ago

4 problems

Riemenschneider's conjecture on special representations of cyclic quotient singularities

Mori–Morrison–Morrison classification conjecture for four-dimensional terminal cyclic quotient singularities

Brohme-Stevens radical ideal conjecture for cyclic quotient deformation spaces

Arndt's Catalan bound for components of cyclic quotient deformation spaces