A compactification of the moduli space of principal Higgs bundles over singular curves

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• 作者：Alessio Lo Giudice^a ; Andrea Pustetto^b ; ^{ex-apustetto@javeriana.edu.co" class="auth_mail" title="E-mail the corresponding author} ; ^{pustetto@gmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 14D20 ; secondary ; 14D22
• 刊名：Journal of Geometry and Physics
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：110
• 期：Complete
• 页码：328-342
• 全文大小：528 K

文摘

A principal Higgs bundle (P,ϕ)$(P,\varphi )$ over a singular curve X$X$ is a pair consisting of a principal bundle P$P$ and a morphism $\varphi :X\to \text{Ad}P\otimes {\Omega }_X^1$. We construct the moduli space of principal Higgs G-bundles over an irreducible singular curve X$X$ using the theory of decorated vector bundles. More precisely, given a faithful representation ρ:G→Sl(V)$\rho :G\to Sl\left(V\right)$ of G$G$, we consider principal Higgs bundles as triples (E,q,φ)$(E,q,\phi )$, where E$E$ is a vector bundle with rk(E)=dimV$\text{rk}\left(E\right)=dimV$ over the normalization $\tilde{X}$ of X$X$, q$q$ is a parabolic structure on E$E$ and φ:E_a,b→L$\phi :E_{a_{},b_{}}\to L$ is a morphism of bundles, L$L$ being a line bundle and E_a,b≑(E^⊗a)^⊕b$E_{a_{},b_{}}\doteqdot {\left(E^{\otimes a}\right)}^{\oplus b}$ a vector bundle depending on the Higgs field ϕ$\varphi$ and on the principal bundle structure.