论文标题
在符号和正交抛物线式希格斯束的模量上进行的Hitchin振动
Hitchin fibration on moduli of symplectic and orthogonal parabolic Higgs bundles
论文作者
论文摘要
令$ x $为紧凑型Riemann属属$ g \ geq 2 $，让$ d \ subset x $为固定有限子集。令$ \ MATHCAL {M}（R，D，α）$表示稳定的抛物线$ G $捆绑包（其中$ g $是$ r $的复杂正交或符号组），度$ r $的复杂正交或符号组），$ D $ $ d $和$ x $的权重$α$。希钦发现，代数曲线上稳定束的模量空间的cotangent束是一个代数完全可以整合的系统，该系统在不变多项式的空间上，既由雅各布式的多项式，也可以由jacobian或prym prim verther频谱曲线进行。在本文中，我们研究了$ \ Mathcal {m}（r，d，α）$的希钦纤维。
Let $X$ be a compact Riemann surface of genus $g \geq 2$, and let $D \subset X$ be a fixed finite subset. Let $\mathcal{M}(r,d,α)$ denote the moduli space of stable parabolic $G$-bundles (where $G$ is a complex orthogonal or symplectic group) of rank $r$, degree $d$ and weight type $α$ over $X$. Hitchin discovered that the cotangent bundle of the moduli space of stable bundles on an algebraic curve is an algebraically completely integrable system fibered, over a space of invariant polynomials, either by a Jacobian or a Prym variety of spectral curves. In this paper we study the Hitchin fibers for $\mathcal{M}(r,d,α)$.
