117 citations · 327 across the 23 of their papers we have counts for
20 papers · 1 filter
Minimal presentations of finite-dimensional representations of pseudocompact algebras
Christof Geiss, Carolin Hartung, Daniel Labardini-Fragoso +1
We give a general formula for minimal projective presentations and for minimal discrete-injective presentations of finite-dimensional modules over basic pseudocompact algebras. We…
Bangle functions are the generic basis for cluster algebras from punctured surfaces with boundary
Christof Geiß, Daniel Labardini-Fragoso, Jon Wilson
We prove that for any possibly-punctured surface with non-empty boundary , and any tagged triangulation of in the sense of Fomi…
Gentle algebras arising from surfaces with orbifold points, Part II: Locally free Caldero-Chapoton functions
Daniel Labardini-Fragoso, Lang Mou
We prove that in the skew-symmetrizable cluster algebras associated by Felikson-Shapiro-Tumarkin to unpunctured surfaces with orbifold points of order and a specific choice of…
Laminations of punctured surfaces as -regular irreducible components
Christof Geiß, Daniel Labardini-Fragoso, Jon Wilson
Let be a surface with marked points on the boundary, and punctures $\mathbb{P}\subsetΣ\setminu…
Semicontinuous maps on module varieties
Christof Geiß, Daniel Labardini-Fragoso, Jan Schröer
We study semicontinuous maps on varieties of modules over finite-dimensional algebras. We prove that truncated Euler maps are upper or lower semicontinuous. This implies that -v…
Landau-Ginzburg potentials via projective representations
Daniel Labardini-Fragoso, Bea Schumann
We interpret the Landau-Ginzburg potentials associated to Gross-Hacking-Keel-Kontsevich's partial compactifications of cluster varieties as F-polynomials of projective representati…
Gentle algebras arising from surfaces with orbifold points of order 3, Part I: scattering diagrams
Daniel Labardini-Fragoso, Lang Mou
To each triangulation of any surface with marked points on the boundary and orbifold points of order three, we associate a quiver (with loops) with potential whose Jacobian algebra…
Quivers with potentials associated to triangulations of closed surfaces with at most two punctures
Jan Geuenich, Daniel Labardini-Fragoso, José Luis Miranda-Olvera
We tackle the classification problem of non-degenerate potentials for quivers arising from triangulations of surfaces in the cases left open by Geiss-Labardini-Schröer. Namely, for…
Generic Caldero-Chapoton functions with coefficients and applications to surface cluster algebras
Christof Geiß, Daniel Labardini-Fragoso, Jan Schröer
We realize Derksen-Weyman-Zelevinsky's mutations of representations as densely-defined regular maps on representation spaces, and study the generic values of Caldero-Chapoton funct…
Derived categories of skew-gentle algebras and orbifolds
Daniel Labardini-Fragoso, Sibylle Schroll, Yadira Valdivieso
Skew-gentle algebras are a generalisation of the well-known class of gentle algebras with which they share many common properties. In this work, using non-commutative Gröbner basis…
Schemes of modules over gentle algebras and laminations of surfaces
Christof Geiß, Daniel Labardini-Fragoso, Jan Schröer
We study the affine schemes of modules over gentle algebras. We describe the smooth points of these schemes, and we also analyze their irreducible components in detail. Several of…
On a family of Caldero-Chapoton algebras that have the Laurent phenomenon
Daniel Labardini-Fragoso, Diego Velasco
We realize a family of generalized cluster algebras as Caldero-Chapoton algebras of quivers with relations. Each member of this family arises from an unpunctured polygon with one o…
Derived invariants for surface cut algebras II: the punctured case
Claire Amiot, Daniel Labardini-Fragoso, Pierre-Guy Plamondon
For each algebra of global dimension 2 arising from the quiver with potential associated to a triangulation of an unpunctured surface, Amiot-Grimeland have defined an integer-value…
The representation type of Jacobian algebras
Christof Geiß, Daniel Labardini-Fragoso, Jan Schröer
We show that the representation type of the Jacobian algebra P(Q,S) associated to a 2-acyclic quiver Q with non-degenerate potential S is invariant under QP-mutations. We prove tha…
On triangulations, quivers with potentials and mutations
Daniel Labardini-Fragoso
In this survey article we give a brief account of constructions and results concerning the quivers with potentials associated to triangulations of surfaces with marked points. Besi…
Caldero-Chapoton algebras
Giovanni Cerulli Irelli, Daniel Labardini-Fragoso, Jan Schröer
Motivated by the representation theory of quivers with potentials introduced by Derksen, Weyman and Zelevinsky and by work of Caldero and Chapoton, who gave explicit formulae for t…
Linear independence of cluster monomials for skew-symmetric cluster algebras
Giovanni Cerulli Irelli, Bernhard Keller, Daniel Labardini-Fragoso +1
Fomin-Zelevinsky conjectured that in any cluster algebra, the cluster monomials are linearly independent and that the exchange graph and cluster complex are independent of the choi…
Quivers with potentials associated to triangulated surfaces, Part III: tagged triangulations and cluster monomials
Giovanni Cerulli Irelli, Daniel Labardini-Fragoso
To each tagged triangulation of a surface with marked points and non-empty boundary we associate a quiver with potential, in such a way that whenever we apply a flip to a tagged tr…
Quivers with potentials associated to triangulated surfaces, Part II: Arc representations
Daniel Labardini-Fragoso
This paper is a representation-theoretic extension of Part I. It has been inspired by three recent developments: surface cluster algebras studied by Fomin-Shapiro-Thurston, the mut…
Quivers with potentials associated to triangulated surfaces
Daniel Labardini-Fragoso
We attempt to relate two recent developments: cluster algebras associated to triangulations of surfaces by Fomin-Shapiro-Thurston, and quivers with potentials and their mutations i…