Integral cohomology of dual boundary complexes is motivic
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917763788832768 |
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| author | Su, Tao |
| author_facet | Su, Tao |
| contents | In this note, we give a motivic characterization of the integral cohomology of dual boundary complexes of smooth quasi-projective complex algebraic varieties. As a corollary, the dual boundary complex of any stably affine space (of positive dimension) is contractible. In a separate paper [Su23], this corollary has been used by the author in his proof of the weak geometric P=W conjecture for very generic $GL_n(\mathbb{C})$-character varieties over any punctured Riemann surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_17301 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Integral cohomology of dual boundary complexes is motivic Su, Tao Algebraic Geometry 14C15 (Primary) 14F45, 14C30 (Secondary) In this note, we give a motivic characterization of the integral cohomology of dual boundary complexes of smooth quasi-projective complex algebraic varieties. As a corollary, the dual boundary complex of any stably affine space (of positive dimension) is contractible. In a separate paper [Su23], this corollary has been used by the author in his proof of the weak geometric P=W conjecture for very generic $GL_n(\mathbb{C})$-character varieties over any punctured Riemann surfaces. |
| title | Integral cohomology of dual boundary complexes is motivic |
| topic | Algebraic Geometry 14C15 (Primary) 14F45, 14C30 (Secondary) |
| url | https://arxiv.org/abs/2408.17301 |