AI 中文总结
研究光滑射影法诺三维流形上潘德哈里潘德 - 托马斯稳定对的后代生成级数，利用壁穿越设置，通过在特定李代数及多项式实现中计算，得出法诺三维流形上一维唐纳森 - 托马斯不变量等。
AI 中文摘要
我们研究光滑射影法诺三维流形上潘德哈里潘德 - 托马斯稳定对的后代生成级数。我们使用作者和乔伊斯在射影 - 线性对栈的乔伊斯李代数\(H_*(\N^{\pl},\Q)\)中开发的壁穿越设置，然后进入格罗斯的多项式实现\(e^{\kappa}\Q[s_{jk\ell}]\)。我们计算法诺三维流形上一维唐纳森 - 托马斯不变量的明确例子，并通过壁穿越计算潘德哈里潘德 - 托马斯稳定对不变量和后代生成级数。我们在\(\PP^3\)、光滑三次三维流形、\(\Bl_p\PP^3\)、\(\Bl_\ell\PP^3\)以及\(X = \PP^1\times\PP^1\)上的射影丛三维流形\(\PP(\OO_X\oplus \OO_X(-1,-1))\)上计算例子。在\(\PP^3\)和三次三维流形的例子中，我们将内在大\(n\)尾部与潘德哈里潘德和莫雷拉的公式进行比较，并表明在共同处理的情况下，差异是洛朗多项式。
英文摘要
We study descendent generating series for Pandharipande--Thomas stable pairs on smooth projective Fano threefolds. We use the wall-crossing setup developed by the author and Joyce in Joyce's Lie algebra $H_*(\N^{\pl},\Q)$ of the projective-linear pairs stack, and next pass to Gross's polynomial realization $e^κ\Q[s_{jk\ell}]$. We compute explicit examples of one-dimensional Donaldson--Thomas invariants on Fano 3-folds and, via wall-crossing, Pandharipande--Thomas stable pair invariants and descendent generating series. We compute examples on $\PP^3$, on a smooth cubic threefold, on $\Bl_p\PP^3$, on $\Bl_\ell\PP^3$, and on the projective-bundle threefold $\PP(\OO_X\oplus \OO_X(-1,-1))$ over $X=\PP^1\times\PP^1$. In the $\PP^3$ and cubic threefold examples we compare the intrinsic large-$n$ tails with the formulas of Pandharipande and Moreira and show that, in the cases treated in common, the differences are Laurent polynomials.
Comments57 pages. Added AI acknowledgements
DOI：10.13140/RG.2.2.35985.70243
