Cross-ratio degrees and triangulations
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913456713629696 |
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| author | Silversmith, Rob |
| author_facet | Silversmith, Rob |
| contents | The cross-ratio degree problem counts configurations of n points on P^1 with n-3 prescribed cross-ratios. Cross-ratio degrees arise in many corners of combinatorics and geometry, but their structure is not well-understood in general. Interestingly, examining various special cases of the problem can yield combinatorial structures that are both diverse and rich. In this paper we prove a simple closed formula for a class of cross-ratio degrees indexed by triangulations of an n-gon; these degrees are connected to the geometry of the real locus of M_{0,n}, and to positive geometry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_07377 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Cross-ratio degrees and triangulations Silversmith, Rob Algebraic Geometry Combinatorics The cross-ratio degree problem counts configurations of n points on P^1 with n-3 prescribed cross-ratios. Cross-ratio degrees arise in many corners of combinatorics and geometry, but their structure is not well-understood in general. Interestingly, examining various special cases of the problem can yield combinatorial structures that are both diverse and rich. In this paper we prove a simple closed formula for a class of cross-ratio degrees indexed by triangulations of an n-gon; these degrees are connected to the geometry of the real locus of M_{0,n}, and to positive geometry. |
| title | Cross-ratio degrees and triangulations |
| topic | Algebraic Geometry Combinatorics |
| url | https://arxiv.org/abs/2310.07377 |