Derived Stratified-Microlocal Framework and Moduli Space Resolution for the Cheeger-Goresky-Macpherson Conjecture
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915485432414208 |
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| author | Luo, Jiaming |
| author_facet | Luo, Jiaming |
| contents | In this paper, We define the stratified metric $\infty$-category $\mathbf{StratMet}_{\infty}$ and the middle perversity moduli stack $\mathscr{M}^{\mathrm{mid}}$. We construct a universal truncation complex $Ω_{X,\mathrm{FS}}^{\bullet,\mathrm{univ}}$ for a projective variety $X\subseteq\mathbb{P}^N$. By introducing the stratified singular characteristic variety $\mathrm{SSH}_{\mathrm{strat}}$, we establish a microlocal correspondence between metric asymptotic behavior and topology, proving the natural isomorphism $$H_2^*(X_{\mathrm{reg}}, ds_{\mathrm{FS}}^2) \cong IH^*(X,\mathbb{C}).$$ This framework transcends transverse singularity constraints, achieves moduli space parametrized duality, and develops new paradigms for high-codimension singular topology, quantum singularity theory, and $p$-adic Hodge theory. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_17833 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Derived Stratified-Microlocal Framework and Moduli Space Resolution for the Cheeger-Goresky-Macpherson Conjecture Luo, Jiaming Algebraic Geometry 2020: 55N33, 14F43 In this paper, We define the stratified metric $\infty$-category $\mathbf{StratMet}_{\infty}$ and the middle perversity moduli stack $\mathscr{M}^{\mathrm{mid}}$. We construct a universal truncation complex $Ω_{X,\mathrm{FS}}^{\bullet,\mathrm{univ}}$ for a projective variety $X\subseteq\mathbb{P}^N$. By introducing the stratified singular characteristic variety $\mathrm{SSH}_{\mathrm{strat}}$, we establish a microlocal correspondence between metric asymptotic behavior and topology, proving the natural isomorphism $$H_2^*(X_{\mathrm{reg}}, ds_{\mathrm{FS}}^2) \cong IH^*(X,\mathbb{C}).$$ This framework transcends transverse singularity constraints, achieves moduli space parametrized duality, and develops new paradigms for high-codimension singular topology, quantum singularity theory, and $p$-adic Hodge theory. |
| title | Derived Stratified-Microlocal Framework and Moduli Space Resolution for the Cheeger-Goresky-Macpherson Conjecture |
| topic | Algebraic Geometry 2020: 55N33, 14F43 |
| url | https://arxiv.org/abs/2508.17833 |