Geometria em Lisboa Seminar   RSS

Alessia Mandini 16/06/2020, 17:00 — 18:00 — Online
, IST and Universidade Federal Fluminense

Quasi-parabolic Higgs bundles and null hyperpolygon spaces

Hyperpolygons spaces are a family of hyperkähler manifolds, that can be obtained from coadjoint orbits by hyperkähler reduction. Jointly with L. Godinho, we showed that these space are isomorphic to certain families of parabolic Higgs bundles, when a suitable condition between the parabolic weights and the spectra of the coadjoint orbits is satisfied.

In analogy to this construction, we introduce two moduli spaces: the moduli spaces of quasi-parabolic $\operatorname{SL}(2,\mathbb{C})$-Higgs bundles over $\mathbb{CP}^1$ on one hand and the null hyperpolygon spaces on the other, and establish an isomorphism between them.

Finally we describe the fixed loci of natural involutions defined on these spaces and relate them to the moduli space of null hyperpolygons in the Minkowski $3$-space.

This is based in joint works with Leonor Godinho.

See also

Slides of the talk

Current organizers: Rosa Sena Dias, José Mourão.
Zoom password: send an email to one of the organizers to ask for the password.