复超曲面奇点类别上的霍奇结构

Michael K. Brown, Mark E. Walker
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引用次数: 0

摘要

给定一个由同次多项式决定孤立奇点的复仿射超曲面,我们将其奇点范畴的周期循环同调上的非交换霍奇结构与相关投影超曲面的基元同调上的经典霍奇结构相提并论。因此,我们证明了投影超曲面的霍奇猜想等同于奇点范畴的霍奇猜想的 dg 类类似物。
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The Hodge structure on the singularity category of a complex hypersurface
Given a complex affine hypersurface with isolated singularity determined by a homogeneous polynomial, we identify the noncommutative Hodge structure on the periodic cyclic homology of its singularity category with the classical Hodge structure on the primitive cohomology of the associated projective hypersurface. As a consequence, we show that the Hodge conjecture for the projective hypersurface is equivalent to a dg-categorical analogue of the Hodge conjecture for the singularity category.
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