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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.12368 |
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| _version_ | 1866912588603850752 |
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| author | Sundbo, Evan |
| author_facet | Sundbo, Evan |
| contents | In this article we introduce the notion of a balloon animal map between broken toric varieties and construct several long exact sequences in cohomology related to them. We give a new proof of the deletion-contraction relation on hypertoric Hitchin systems of Dansco-Mcbreen-Shende and present some refinements of it. The end result is a formula for the Poincaré polynomial of any hypertoric Hitchin system associated to a graph with first Betti number 2 along with a recipe to calculate the Poincaré polynomial of any hypertoric Hitchin system, given knowledge of a finite number of base cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_12368 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Balloon Animal Maps with Applications to the Cohomology of Hypertoric Hitchin Systems Sundbo, Evan Algebraic Geometry In this article we introduce the notion of a balloon animal map between broken toric varieties and construct several long exact sequences in cohomology related to them. We give a new proof of the deletion-contraction relation on hypertoric Hitchin systems of Dansco-Mcbreen-Shende and present some refinements of it. The end result is a formula for the Poincaré polynomial of any hypertoric Hitchin system associated to a graph with first Betti number 2 along with a recipe to calculate the Poincaré polynomial of any hypertoric Hitchin system, given knowledge of a finite number of base cases. |
| title | Balloon Animal Maps with Applications to the Cohomology of Hypertoric Hitchin Systems |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2509.12368 |