Configurations of 10 points and their incidence varieties
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arXiv
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| Hauptverfasser: | , , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908448724090880 |
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| author | Isham, Kelly Kaplan, Nathan Kimport, Sam Lawrence, Rachel Peilen, Luke Weinreich, Max |
| author_facet | Isham, Kelly Kaplan, Nathan Kimport, Sam Lawrence, Rachel Peilen, Luke Weinreich, Max |
| contents | Incidence varieties are spaces of $n$-tuples of points in the projective plane that satisfy a given set of collinearity conditions. We classify the components of incidence varieties and realization moduli spaces associated to configurations of up to 10 points, up to birational equivalence. We show that each realization space component is birational to a projective space, a genus 1 curve, or a K3 surface. To do this, we reduce the problem to a study of 163 special arrangements called superfigurations. Then we use computer algebra to describe the realization space of each superfiguration. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_09829 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Configurations of 10 points and their incidence varieties Isham, Kelly Kaplan, Nathan Kimport, Sam Lawrence, Rachel Peilen, Luke Weinreich, Max Algebraic Geometry 14N20, 14J10, 51A20 Incidence varieties are spaces of $n$-tuples of points in the projective plane that satisfy a given set of collinearity conditions. We classify the components of incidence varieties and realization moduli spaces associated to configurations of up to 10 points, up to birational equivalence. We show that each realization space component is birational to a projective space, a genus 1 curve, or a K3 surface. To do this, we reduce the problem to a study of 163 special arrangements called superfigurations. Then we use computer algebra to describe the realization space of each superfiguration. |
| title | Configurations of 10 points and their incidence varieties |
| topic | Algebraic Geometry 14N20, 14J10, 51A20 |
| url | https://arxiv.org/abs/2507.09829 |