Centro de Matemática

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20012022

most citedAutomated polyp detection in colon capsule endoscopy

306 citations

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21 papers · 1 filter

math.AG2021★ 6 cited

Lie algebroid connections, twisted Higgs bundles and motives of moduli spaces

David Alfaya, André Oliveira

Let $L = (L, [\cdot, \cdot], δ)$ be an algebraic Lie algebroid over a smooth projective curve $X$ of genus $g \geq 2$ such that $L$ is a line bundle whose degree is less than…

math.AG2020

Stratifications on the Nilpotent Cone of the moduli space of Hitchin pairs

Peter B. Gothen, Ronald A. Zúñiga-Rojas

We consider the problem of finding the limit at infinity (corresponding to the downward Morse flow) of a Higgs bundle in the nilpotent cone under the natural $C^{*}$ -action…

math.AG2018★ 3 cited

Homotopy Type of Moduli Spaces of G-Higgs Bundles and Reducibility of the Nilpotent Cone

C. Florentino, P. B. Gothen, A. Nozad

Let $G$ be a real reductive Lie group, and $H^{C}$ the complexification of its maximal compact subgroup $H \subset G$ . We consider classes of semistable $G$ -Higgs bundles o…

math.AG2018★ 13 cited

SO(p,q)-Higgs bundles and higher Teichmüller components

Marta Aparicio-Arroyo, Steven Bradlow, Brian Collier +3

Some connected components of a moduli space are mundane in the sense that they are distinguished only by obvious topological invariants or have no special characteristics. Others a…

math.AG2018★ 17 cited

Unramified covers and branes on the Hitchin system

Emilio Franco, Peter Gothen, André Oliveira +1

We study the locus of the moduli space of Higgs bundles on a curve given by those Higgs bundles obtained by pushforward under an unramified cover. We equip these loci with a hyperh…

math.AG2018★ 8 cited

Exotic components of $SO (p, q)$ surface group representations, and their Higgs bundle avatars

Marta Aparicio-Arroyo, Steven Bradlow, Brian Collier +3

For semisimple Lie groups, moduli spaces of Higgs bundles on a Riemann surface correspond to representation varieties for the surface fundamental group. In many cases, natural topo…

math.AG2017★ 2 cited

Quiver Bundles and Wall Crossing for Chains

P. B. Gothen, A. Nozad

Holomorphic chains on a Riemann surface arise naturally as fixed points of the natural C*-action on the moduli space of Higgs bundles. In this paper we associate a new quiver bundl…

math.AG2017★ 21 cited

Topological mirror symmetry for parabolic Higgs bundles

Peter B. Gothen, André G. Oliveira

We prove the topological mirror symmetry conjecture of Hausel-Thaddeus for the moduli space of strongly parabolic Higgs bundles of rank two or three, with full flags. Although the…

math.AG2017★ 9 cited

A pair of rigid surfaces with $p_{g} = q = 2$ and $K^{2} = 8$ whose universal cover is not the bidisk

Francesco Polizzi, Carlos Rito, Xavier Roulleau

We construct two complex-conjugated rigid surfaces with $p_{g} = q = 2$ and $K^{2} = 8$ whose universal cover is not biholomorphic to the bidisk. We show that these are the unique surfaces w…

math.AG2017★ 9 cited

Irreducibility of moduli of semistable Chains and applications to U(p,q)-Higgs bundles

Steven Bradlow, Oscar Garcia-Prada, Peter Gothen +1

We give necessary and sufficient conditions for moduli spaces of semistable chains on a curve to be irreducible and non-empty. This gives information on the irreducible components…

math.AG2016★ 5 cited

Birationality of moduli spaces of twisted $U (p, q)$ -Higgs bundles

Peter B. Gothen, Azizeh Nozad

A $U (p, q)$ -Higgs bundle on a Riemann surface (twisted by a line bundle) consists of a pair of holomorphic vector bundles, together with a pair of (twisted) maps between th…

math.AG2015★ 7 cited

Compactified universal jacobian and the double ramification cycle

Bashar Dudin

Using the compactified universal jacobian over the moduli space of stable marked curves, we give an expression in terms of natural classes of the zero section of the compactified u…

math.AG2015★ 12 cited

Branes in the moduli space of framed instantons

Emilio Franco, Marcos Jardim, Simone Marchesi

In the physicist's language, a brane in a hyperkahler manifold is a submanifold which is either complex or lagrangian with respect to three Kahler structures of the ambient manif…

math.AG2014★ 1 cited

Algebraic and combinatorial rank of divisors on finite graphs

Lucia Caporaso, Yoav Len, Margarida Melo

We study the algebraic rank of a divisor on a graph, an invariant defined using divisors on algebraic curves dual to the graph. We prove it satisfies the Riemann-Roch formula, a sp…

math.AG2013★ 20 cited

Fourier-Mukai and autoduality for compactified Jacobians II

Margarida Melo, Antontio Rapagnetta, Filippo Viviani

To every reduced (projective) curve X with planar singularities one can associate many fine compactified Jacobians, depending on the choice of a polarization on X, which are birati…

math.AG2013★ 11 cited

Higgs bundles for the non-compact dual of the special orthogonal group

Steven B. Bradlow, Oscar Garcia-Prada, Peter B. Gothen

Higgs bundles over a closed orientable surface can be defined for any real reductive Lie group G. In this paper we examine the case G=SO*(2n). We describe a rigidity phenomenon enc…

math.AG2011★ 11 cited

Rank two quadratic pairs and surface group representations

Peter B. Gothen, André Oliveira

Let $X$ be a compact Riemann surface. A quadratic pair on $X$ consists of a holomorphic vector bundle with a quadratic form which takes values in fixed line bundle. We show that th…

math.AG2010★ 13 cited

The singular fibre of the Hitchin map

Peter B. Gothen, André Oliveira

Given any line bundle L of positive degree, on a compact Riemann surface, let $M_{L}^{Λ}$ be the moduli space of L-twisted Higgs pairs of rank 2 with fixed determinant isomorphic to $Λ…

math.AG2010★ 25 cited

Fine compactified Jacobians

Margarida Melo, Filippo Viviani

We study Esteves's fine compactified Jacobians for nodal curves. We give a proof of the fact that, for a one-parameter regular local smoothing of a nodal curve $X$ , the relative sm…

math.AG2009★ 17 cited

Parallel Kustin--Miller unprojection with an application to Calabi--Yau geometry

Jorge Neves, Stavros Argyrios Papadakis

Kustin--Miller unprojection constructs more complicated Gorenstein rings from simpler ones. Geometrically, it inverts certain projections, and appears in the constructions of expli…

math.AG2008★ 62 cited

Higgs bundles and surface group representations in the real symplectic group

Oscar Garcia-Prada, Peter B. Gothen, Ignasi Mundet i Riera

In this paper we study the moduli space of representations of a surface group (i.e., the fundamental group of a closed oriented surface) in the real symplectic group Sp(2n,R). The…