arXiv subjects

Marina Godinho

Publications and source records attributed to Marina Godinho.

4 recordsLinked to original sources

arXiv2026

A twist on ring morphisms and crepant contractions

Given a ring morphism, this paper constructs the twist functor around the induced derived restriction of scalars functor. We prove that the twist around ring morphisms is a derived autoequivalence in the setting of twists induced by Frobenius exact categories. As a corollary, it is shown that the noncommutative twist introduced by Donovan and Wemyss is in fact a spherical twist around the restriction of scalars functor. We then use this technology to obtain new spherical twists for singular schemes, and discuss how our result extends previous works on spherical twists induced by crepant contractions.

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arXiv2026

Spherical Twists for Gorenstein Orders and $G$-Hilb

This paper constructs derived autoequivalences of Gorenstein orders as twists around spherical functors. More precisely, given a Gorenstein order $A$ and a quotient $p \colon A \to B$, then we specify natural conditions on $B$ under which the twist around the corresponding derived restriction of scalars functor is a derived autoequivalence of $A$. In the process, we show that the associated cotwist is a shift of the Nakayama functor of $B$. These results, together with local-to-global technology, are then used construct new derived autoequivalences for skew group algebras and $G$-Hilbert schemes, and we apply this theory to explicit examples.

math.RT↗

arXiv2026

Extended Admissible Dissections of Marked Surfaces and Piano Algebras

We introduce the notion of extended admissible dissections of a marked surface, building upon the notion of an admissible dissection of a marked surface by Amiot--Plamondon--Schroll. For each extended admissible dissection we construct a differential graded algebra, called a piano algebra, which may be viewed in some sense as a differential graded analogue of a gentle algebra. We show that for a marked disc without punctures, a piano algebra is quasi-isomorphic to the graded endomorphism ring of a classical generator of the Paquette--Yıldırım completion of the discrete cluster category of Dynkin type $A_{\infty}$, labelled $\overline{\mathcal{C}}_n$. We use previous results of the authors to show that there exists an additive equivalence between $\overline{\mathcal{C}}_n$ and the perfect derived category of a specific piano algebra, that sends triangles with two indecomposable terms to triangles with two indecomposable terms. We use this equivalence to prove that any two piano algebras coming from homeomorphic marked discs are derived equivalent.

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arXiv2025

Triangulated Categories Admitting Linear Generators

The main result of this paper is that there is an additive equivalence between $\overline{\mathcal{C}}_n$, the Paquette-Yildirim completion of the discrete cluster categories of Dynkin type $A_{\infty}$, and the perfect derived category of a certain DG algebra. This additive equivalence preserves some of the triangulated structure: it commutes with the suspension functor and preserves triangles with at least two indecomposable terms. In the process, we introduce the notion of a linear generator $G$ in a Krull-Schmidt, Hom-finite triangulated category. It turns out that the existence of a linear generator affords a large amount of control over $\mathcal{T}$. For example, it allows us to describe all indecomposable objects in $\mathcal{T}$ in terms of $G$, to determine all triangles of $\mathcal{T}$ with at least two indecomposable objects, and to show that the Rouquier dimension of $\mathcal{T}$ is at most one. Moreover, we prove that there is an additive equivalence (which preserves some of the triangulated structure) between $\mathcal{T}$ and the perfect derived category of a certain DG algebra. Finally, we show that any triangulated category with a linear generator is additively equivalent to a thick subcategory of $\overline{\mathcal{C}}_n$.

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