The Hodge structure on the singularity category of a complex hypersurface
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911106394488832 |
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| author | Brown, Michael K. Walker, Mark E. |
| author_facet | Brown, Michael K. Walker, Mark E. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_09988 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Hodge structure on the singularity category of a complex hypersurface Brown, Michael K. Walker, Mark E. Algebraic Geometry Commutative Algebra K-Theory and Homology 13D03, 13D09, 14C30, 14F08, 14J70, 19D55 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. |
| title | The Hodge structure on the singularity category of a complex hypersurface |
| topic | Algebraic Geometry Commutative Algebra K-Theory and Homology 13D03, 13D09, 14C30, 14F08, 14J70, 19D55 |
| url | https://arxiv.org/abs/2407.09988 |