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Lecture 1 : Introduction to the spectral construction and Higgs bundles

Le : 23/09/2014 11h00
Par : Peter Dalakov (Academie des Sciences, Sophia, Boulgarie)
Lieu : I 001
Lien web :
Résumé : In this talk we shall review the spectral construction and some applications. In its basic form, this is the idea of converting the data of a family of regular endomorphisms of a vector space into the data of a "spectral cover" and a line bundle on it. We discuss two modifications of the basic setup: 1) Endomorphisms of a vector bundle (over a complex algebraic variety) with coefficients in another vector bundle 2) Sections of the adjoint bundle of a principal G-bundle, for G a simple (or reductive) complex Lie group Item 1) leads to the notion of Higgs (vector) bundle with coefficients. We focus on item 2), and discuss G-Higgs bundles on a smooth algebraic curve and their associated cameral covers. Finally, we discuss some global properties of moduli spaces of Higgs bundles on curves and applications.