arXiv subjects

Marina Godinho

Publications and source records attributed to Marina Godinho.

4 recordsLinked to original sources

arXiv2026

Triangulated Categories Admitting Linear Generators

We introduce the notion of a $w$-linear generator in a $k$-linear, Hom-finite, Krull-Schmidt algebraic triangulated category $\mathcal{T}$ over a field $k$, for some positive integer $w$. We show that the existence of a $w$-linear generator gives us a complete classification of indecomposable objects and morphisms spaces in $\mathcal{T}$, as well as the factorisation of morphisms. We compute the graded endomorphism ring $Λ$ of a $w$-linear generator viewed as a differential graded algebra with trivial differential, and the Hochschild cohomology of $Λ$. It turns out that the graded endomorphism ring of a $w$-linear generator is intrinsically formal, and so $\mathcal{T}$ is triangle equivalent to the perfect derived category of $Λ$. As a application of these results, we find a description of the Paquette--Yıldırım completion of discrete cluster categories of type $A_{\infty}$ as a perfect derived category. Further, we confirm a conjecture of Franchini in her PhD thesis, and show that the $(w+1)$-Calabi--Yau candidate categories she introduces are in fact triangulated categories.

math.RT↗

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.

math.AG↗

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.

math.RT↗