Hilbert格式与khovanov - rozansky同调的y化

E. Gorsky, Matthew Hogancamp
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引用次数: 20

摘要

作者:戈尔斯基,尤金;摘要:我们定义了一个连杆$L$的三阶Khovanov-Rozansky同调的变形,该变形依赖于$L$的每个分量的参数$y_c$的选择,它满足类似于Batson-Seed不变量的链路分裂性质。保持$y_c$作为形式变量,在$\mathbb{Q}[x_c,y_c]_{c\in \pi_0(L)}$上的三重分级模块中产生链接同调值。我们推测这个不变量恢复了三阶Khovanov-Rozansky同调中缺失的$Q\leftrightarrow TQ^{-1}$对称性,并且还满足了一些来自与平面上点的Hilbert格式的猜想联系的预测。我们计算了全扭转的所有正幂的不变量,并将其与海曼描述的等谱希尔伯特格式中的理想族相匹配。
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Hilbert schemes and y–ification of Khovanov–Rozansky homology
Author(s): Gorsky, Eugene; Hogancamp, Matthew | Abstract: We define a deformation of the triply graded Khovanov-Rozansky homology of a link $L$ depending on a choice of parameters $y_c$ for each component of $L$, which satisfies link-splitting properties similar to the Batson-Seed invariant. Keeping the $y_c$ as formal variables yields a link homology valued in triply graded modules over $\mathbb{Q}[x_c,y_c]_{c\in \pi_0(L)}$. We conjecture that this invariant restores the missing $Q\leftrightarrow TQ^{-1}$ symmetry of the triply graded Khovanov-Rozansky homology, and in addition satisfies a number of predictions coming from a conjectural connection with Hilbert schemes of points in the plane. We compute this invariant for all positive powers of the full twist and match it to the family of ideals appearing in Haiman's description of the isospectral Hilbert scheme.
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