20 citations · 35 across the 14 of their papers we have counts for
19 papers
Extending Andreotti's proof of Torelli's theorem to nodal curves
Alex Abreu, Marco Pacini, Nicola Pagani
Let be a connected nodal curve of genus over an algebraically closed field of characteristic zero. Let \[ A(C)=\Big(J(C), {\overline{P^{g-1}_C}}, Θ(C) \Big) \] be the s…
A Torelli theorem for graphs via quasistable divisors
Alex Abreu, Marco Pacini
The Torelli theorem establishes that the Jacobian of a smooth projective curve, together with the polarization provided by the theta divisor, fully characterizes the curve. In the…
Splitting the cohomology of Hessenberg varieties and e-positivity of chromatic symmetric functions
Alex Abreu, Antonio Nigro
For each indifference graph, there is an associated regular semisimple Hessenberg variety, whose cohomology recovers the chromatic symmetric function of the graph. The decompositio…
Wall-crossing of universal Brill-Noether classes
Alex Abreu, Nicola Pagani
We give an explicit graph formula, in terms of decorated boundary strata classes, for the wall-crossing of universal Brill-Noether classes. More precisely, fix n>0 and d<g , and tw…
Parabolic Lusztig varieties and chromatic symmetric functions
Alex Abreu, Antonio Nigro
The characters of Kazhdan--Lusztig elements of the Hecke algebra over (and in particular, the chromatic symmetric function of indifference graphs) are completely encoded in t…
A geometric approach to characters of Hecke algebras
Alex Abreu, Antonio Nigro
To any element of a connected, simply connected, semisimple complex algebraic group G and a choice of an element of the corresponding Weyl group there is an associated Lusztig vari…
An update on Haiman's conjectures
Alex Abreu, Antonio Nigro
We revisit Haiman's conjecture on the relations between characters of Kazdhan-Lusztig basis elements of the Hecke algebra over the symmetric group. The conjecture asserts that, for…
On moduli spaces of roots in algebraic and tropical geometry
Alex Abreu, Marco Pacini, Matheus Secco
In this paper we construct a tropical moduli space parametrizing roots of divisors on tropical curves. We study the relation between this space and the skeleton of Jarvis moduli sp…
Degree-2 Abel maps and hyperelleptic curves
Alex Abreu, Sally Andria, Marco Pacini
In this paper we resolve the degree-2 Abel map for nodal curves. Our results are based on a previous work of the authors reducing the problem of the resolution of the Abel map to a…
The moduli space of quasistable spin curves
Alex Abreu, Marco Pacini, Danny Taboada
We study a compactification of the moduli space of theta characteristics, giving a modular interpretation of the geometric points and describing the boundary stratification. This s…
Abel Maps for nodal curves via tropical geometry
Alex Abreu, Sally Andria, Marco Pacini
We consider Abel maps for regular smoothing of nodal curves with values in the Esteves compactified Jacobian. In general, these maps are just rational, and an interesting question…
Chromatic symmetric functions from the modular law
Alex Abreu, Antonio Nigro
In this article we show how to compute the chromatic quasisymmetric function of indifference graphs from the modular law introduced by Guay-Paquet. We provide an algorithm which wo…
A symmetric function of increasing forests
Alex Abreu, Antonio Nigro
For an indifference graph we define a symmetric function of increasing spanning forests of . We prove that this symmetric function satisfies certain linear relations, which…
A universal tropical Jacobian over $M_g^{\trop}$
Alex Abreu, Sally Andria, Marco Pacini +1
We introduce and study polystable divisors on a tropical curve, which are the tropical analogue of polystable torsion-free rank-1 sheaves on a nodal curve. We construct a universal…
The resolution of the universal Abel map via tropical geometry and applications
Alex Abreu, Marco Pacini
Let and be nonnegative integers and a sequence of integers summing up to . Let be the moduli space of…
The universal tropical Jacobian and the skeleton of the Esteves' universal Jacobian
Alex Abreu, Marco Pacini
For each universal genus- polarization of degree , we construct a universal tropical Jacobian as a generalized cone complex over the moduli space of stab…
The automorphism group of and
Alex Abreu, Marco Pacini
In this paper we show that the automorphism groups of and are isomorphic to the permutation group for , whi…
Enriched curves and their tropical counterpart
Alex Abreu, Marco Pacini
In her Ph.D. thesis, Mainò introduced the notion of enriched structure on stable curves and constructed their moduli space. In this paper we give a tropical notion of enriched stru…
On the geometry of Abel maps for nodal curves
Alex Abreu, Juliana Coelho, Marco Pacini
In this paper we give local conditions to the existence of Abel maps for nodal curves that are limits of Abel maps for smooth curves. We use this result to construct Abel maps for…