Type: Seminar

Distribution: World

CalTitle1: Cliff - On the Kirwan map for moduli stacks of Higgs bundles

Auth: romanova@10.17.26.183 (arom8272) in SMS-SAML

To a reductive group G and a smooth projective complex curve C, one associates the moduli stack of G-Higgs bundles on C. There is a natural map from the cohomology of the moduli stack of G-Higgs bundles to the cohomology of the moduli stack of semistable G-Higgs bundles, known as the Kirwan map. In the case of G=GL(n), Markman proved that the Kirwan map is surjective for the component of Higgs bundles of degree d coprime to n. By contrast, I explain recent work in which we show (generalizing Hitchin for SL(n)) that the Kirwan map for moduli of G-Higgs bundles fails to be surjective whenever G has disconnected centre. This is accomplished via the study of a group action on the moduli stack and the induced action on its cohomology. This talk is based on joint work with Thomas Nevins and Shiyu Shen. I will not assume the audience has background knowledge on stacks or Higgs bundles.