Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.20466 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912991053611008 |
|---|---|
| author | Chen, Dawei Chen, Qile |
| author_facet | Chen, Dawei Chen, Qile |
| contents | Multiscale differentials arise as limits of holomorphic differentials with prescribed zero orders on nodal curves. In this paper, we address the conjecture concerning Gorenstein contractions of multiscale differentials, originally proposed by Ranganathan and Wise and further developed by Battistella and Bozlee. Specifically, in the case of a one-parameter degeneration, we show that multiscale differentials can be contracted to Gorenstein singularities, level by level, from the top down. At each level, these differentials descend to generators of the dualizing bundle at the resulting singularities. Moreover, the global residue condition, which governs the smoothability of multiscale differentials, appears as a special case of the residue condition for descent differentials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_20466 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Gorenstein contractions of multiscale differentials Chen, Dawei Chen, Qile Algebraic Geometry Geometric Topology Multiscale differentials arise as limits of holomorphic differentials with prescribed zero orders on nodal curves. In this paper, we address the conjecture concerning Gorenstein contractions of multiscale differentials, originally proposed by Ranganathan and Wise and further developed by Battistella and Bozlee. Specifically, in the case of a one-parameter degeneration, we show that multiscale differentials can be contracted to Gorenstein singularities, level by level, from the top down. At each level, these differentials descend to generators of the dualizing bundle at the resulting singularities. Moreover, the global residue condition, which governs the smoothability of multiscale differentials, appears as a special case of the residue condition for descent differentials. |
| title | Gorenstein contractions of multiscale differentials |
| topic | Algebraic Geometry Geometric Topology |
| url | https://arxiv.org/abs/2405.20466 |