自同构层，谱覆盖，Kostant和Steinberg截面
Automorphism sheaves, spectral covers, and the Kostant and Steinberg sections
摘要：
Kostant构造了一个简单李代数的伴随商态射到正则元素的开集的部分，Steinberg构造了一个单连通单代数群的伴随商的部分。在本文中，我们证明了伴随商的所有部分是共轭的通过一个态射从伴随商到群。特别地，通过抛物线构造构造的截面与Kostant截面或Steinberg截面共轭。证明方法是研究尖点或节面三次曲线族上某些主丛的自同构层。
英文摘要：
Kostant constructed a section from the adjoint quotient morphism of a simple Lie algebra to the open set of regular elements, and Steinberg constructed such a section for the adjoint quotient of a simply connected and simple algebraic group. In this paper, we show that all sections of the adjoint quotient are conjugate via a morphism from the adjoint quotient to the group. In particular, the sections constructed via the parabolic construction are conjugate either to the Kostant section or to the Steinberg section. The method of proof consists in studying automorphism sheaves of certain principle bundles over faamilies of cuspidal or nodal plane cubic curves.
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