典范扩张的调节器是挠群：两个横截相交的光滑除子的情形
Regulators of canonical extensions are torsion:the case of two transversally intersecting smooth divisors
AI总结：
该研究将平坦丛的Deligne典范扩张的Chern-Simons调节器类为挠群的结论，从单光滑除子推广到两个横截相交光滑除子的情形，相关成果由另一预印本处理完全正常交叉情形。
AI中文摘要：
本注将文献[IS]2007年的主要成果——具有无穷远幂单单值化的平坦丛的Deligne典范扩张的扩张Chern–Simons（调节器）类是挠群——从光滑不可约边界除子的情形推广到边界除子D=D₁∪D₂的情形，其中D₁、D₂是两个光滑不可约分支，沿光滑中心Z=D₁∩D₂横截相交。设X是定义在复数域ℂ上的光滑射影簇，U:=X-D。给定U上具有D各分支附近幂单单值化的平坦丛(E,∇)，考虑X上的Deligne典范扩张(Ē,∇̄)，则对p≥2，扩张Chern-Simons类cₚ(Ē,∇̄)∈H²ᵖ⁻¹(X,ℂ/ℤ)是挠群。本注撰写于2009-2010年，预印本文献[IS2]2026年的成果通过不同方法处理了完全正常交叉的情形。
英文摘要：
This note extends the main result of \cite{IS} 2007 --- torsion of the extended Chern--Simons (regulator) classes of the Deligne canonical extension of a flat bundle with unipotent monodromy at infinity --- from the case of a smooth irreducible boundary divisor to the case of a boundary divisor $D = D_1\cup D_2$ with two smooth irreducible components meeting transversally along a smooth center $Z=D_1\cap D_2$. Let $X$ be a smooth projective variety defined over $\mathbb{C}$, and $U:=X-D$. Given a flat bundle $(E,\nabla)$ on $U$ with unipotent monodromy around the components of $D$ consider Deligne's canonical extension $(\overline{E},\overline{\nabla})$ on $X$. Then the extended Chern-Simons classes $$ c_p(\overline{E},\overline{\nabla})\in H^{2p-1}(X,\mathbb{C}/\mathbb{Z}) $$ are torsion, for $p\geq 2$. These notes were prepared in 2009-2010, and the preprint \cite[2026]{IS2} treats the full normal crossing case via a different approach.
