Rank one Higgs bundles and representations of fundamental groups of Riemann surfaces
著者
書誌事項
Rank one Higgs bundles and representations of fundamental groups of Riemann surfaces
（Memoirs of the American Mathematical Society, no. 904）
American Mathematical Society, 2008
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注記
Includes bibliographical references (p. 67-69)
内容説明・目次
内容説明
This expository article details the theory of rank one Higgs bundles over a closed Riemann surface $X$ and their relation to representations of the fundamental group of $X$. The authors construct an equivalence between the deformation theories of flat connections and Higgs pairs. This provides an identification of moduli spaces arising in different contexts. The moduli spaces are real Lie groups. From each context arises a complex structure, and the different complex structures define a hyperkahler structure. The twistor space, real forms, and various group actions are computed explicitly in terms of the Jacobian of $X$. The authors describe the moduli spaces and their geometry in terms of the Riemann period matrix of $X$.
目次
Introduction Equivalences of deformation theories The Betti and de Rham deformation theories and their moduli spaces The Dolbeault groupoid Equivalence of de Rham and Dolbeault groupoids Hyperkahler geometry on the moduli space The twistor space The moduli space and the Riemann period matrix Bibliography.
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