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摘要翻译：
本文报道了与C.Simpson共同完成的关于Reznikov定理的推广的工作，该定理说光滑复射影簇上平坦向量丛的Chern-Simons类，特别是Deligne Chern类(>1$)是扭转的。考虑了光滑拟射影簇在无穷远处具有不可约光滑因子的情形。定义了无穷远处具有单幂单数的平面向量丛的Deligne\textit{规范扩张}的Chern-Simons类，它提升了Deligne-Chern类，并证明了这些类是扭转的。证明的细节可以在arXIV:0707.0372[Math.ag]中找到。
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英文标题：
《A report on "Regulators of canonical extension are torsion; the smooth
divisor case"》
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作者：
Jaya NN Iyer
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最新提交年份：
2008
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分类信息：
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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一级分类：Mathematics 数学
二级分类：Differential Geometry 微分几何
分类描述：Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis
复形，接触，黎曼，伪黎曼和Finsler几何，相对论，规范理论，整体分析
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英文摘要：
In this note, we report on a work jointly done with C. Simpson on a generalization of Reznikov's theorem which says that the Chern-Simons classes and in particular the Deligne Chern classes (in degrees $> 1$) are torsion, of a flat vector bundle on a smooth complex projective variety. We consider the case of a smooth quasi--projective variety with an irreducible smooth divisor at infinity. We define the Chern-Simons classes of the Deligne's \textit{canonical extension} of a flat vector bundle with unipotent monodromy at infinity, which lift the Deligne Chern classes and prove that these classes are torsion. The details of the proof can be found in arxiv:0707.0372 [math.AG].
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PDF链接：
https://arxiv.org/pdf/0803.1348
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