Thema der Dissertation:
Character Varieties for Seifert Groups and Higgs Bundles over Orbifolds Thema der Disputation:
Spectral correspondence in higher dimensions
Character Varieties for Seifert Groups and Higgs Bundles over Orbifolds Thema der Disputation:
Spectral correspondence in higher dimensions
Abstract: Guided by the non-abelian Hodge theorem, we explore the link between Higgs bundles and spectral geometry on a smooth proper algebraic variety $X$ of dimension $d$. We describe the Hitchin fibration, mapping Higgs bundles on $X$ to a base space $A$ of spectral data. For curves ($d =1$), generic fibers of the Hitchin map are abelian varieties (line bundles on spectral curves), yielding a celebrated completely integrable system.
In higher dimensions, the geometry is governed by a universal spectral cover: Higgs data corresponds to a tuple of commuting endomorphisms and the invariant-theoretic problem is resolved by the joint spectrum of these operators, giving a universal spectral data map. Combining this with the Weyl embedding, we describe the Hitchin map intrinsically and construct spectral covers over $X$. These covers are not flat in general obstructing the surjectivity of the Hitchin map. Chen and Ngo overcome this for surfaces via Cohen-Macaulification of the spectral cover, recovering a geometric description of the generic fibers of the Hitchin map.
In higher dimensions, the geometry is governed by a universal spectral cover: Higgs data corresponds to a tuple of commuting endomorphisms and the invariant-theoretic problem is resolved by the joint spectrum of these operators, giving a universal spectral data map. Combining this with the Weyl embedding, we describe the Hitchin map intrinsically and construct spectral covers over $X$. These covers are not flat in general obstructing the surjectivity of the Hitchin map. Chen and Ngo overcome this for surfaces via Cohen-Macaulification of the spectral cover, recovering a geometric description of the generic fibers of the Hitchin map.
Zeit & Ort
24.06.2025 | 16:15
Seminarraum 115
(Fachbereich Mathematik und Informatik, Arnimallee 3, 14195 Berlin)