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André G. Oliveira

Publications and source records attributed to André G. Oliveira.

2 recordsLinked to original sources
arXiv2023

Narasimhan--Ramanan branes and wobbly Higgs bundles

Narasimhan--Ramanan branes were introduced by the authors in a previous article. They consist of a family of $BBB$-branes inside the moduli space of Higgs bundles, and a family of complex Lagrangian subvarieties. It was conjectured that these complex Lagrangian subvarieties support the $BAA$-branes that are mirror dual to the Narasimhan--Ramanan $BBB$-branes. In this article we show that the support of these branes intersects non-trivially the locus of wobbly Higgs bundles.

math.AG↗
arXiv2018

Topological mirror symmetry for parabolic Higgs bundles

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 main theorem is proved only for rank at most three, most of the results are proved for any prime rank.

math.AG↗