On the Hilbert-Chow crepant resolution conjecture
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866918274125529088 |
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| author | Nesterov, Denis |
| author_facet | Nesterov, Denis |
| contents | We prove the Hilbert-Chow crepant resolution conjecture in the exceptional curve classes for all projective surfaces and all genera. In particular, this confirms Ruan's cohomological Hilbert-Chow crepant resolution conjecture. The proof exploits Fulton-MacPherson compactifications, reducing the conjecture to the case of the affine plane. As an application, using previous results of the author, we also deduce the families DT/GW correspondence for threefolds $S \times C$ in classes that are zero on the first factor, yielding a wall-crossing proof of the correspondence in this case. Finally, we speculate on the relationship between Hilbert schemes and Fulton-MacPherson compactifications beyond the topics considered in this work. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_03036 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the Hilbert-Chow crepant resolution conjecture Nesterov, Denis Algebraic Geometry We prove the Hilbert-Chow crepant resolution conjecture in the exceptional curve classes for all projective surfaces and all genera. In particular, this confirms Ruan's cohomological Hilbert-Chow crepant resolution conjecture. The proof exploits Fulton-MacPherson compactifications, reducing the conjecture to the case of the affine plane. As an application, using previous results of the author, we also deduce the families DT/GW correspondence for threefolds $S \times C$ in classes that are zero on the first factor, yielding a wall-crossing proof of the correspondence in this case. Finally, we speculate on the relationship between Hilbert schemes and Fulton-MacPherson compactifications beyond the topics considered in this work. |
| title | On the Hilbert-Chow crepant resolution conjecture |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2601.03036 |