Varieties of Lines in 3-Space
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911288188207104 |
|---|---|
| author | Hollering, Benjamin Mazzucchelli, Elia Parisi, Matteo Sturmfels, Bernd |
| author_facet | Hollering, Benjamin Mazzucchelli, Elia Parisi, Matteo Sturmfels, Bernd |
| contents | We consider configurations of lines in 3-space with incidences prescribed by a graph. This defines a subvariety in a product of Grassmannians. Leveraging a connection with rigidity theory in the plane, for any graph, we determine the dimension of the incidence variety and characterize when it is irreducible or a complete intersection. We study its multidegree and the family of Schubert problems it encodes. Our spanning-tree coordinates enable efficient symbolic computations. We also provide numerical irreducible decompositions for incidence varieties with up to eight lines. These constructions with lines play a key role in the Landau analysis of scattering amplitudes in particle physics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_21333 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Varieties of Lines in 3-Space Hollering, Benjamin Mazzucchelli, Elia Parisi, Matteo Sturmfels, Bernd Combinatorics High Energy Physics - Theory Commutative Algebra Algebraic Geometry 13P25, 14N20, 14N15, 14J81 We consider configurations of lines in 3-space with incidences prescribed by a graph. This defines a subvariety in a product of Grassmannians. Leveraging a connection with rigidity theory in the plane, for any graph, we determine the dimension of the incidence variety and characterize when it is irreducible or a complete intersection. We study its multidegree and the family of Schubert problems it encodes. Our spanning-tree coordinates enable efficient symbolic computations. We also provide numerical irreducible decompositions for incidence varieties with up to eight lines. These constructions with lines play a key role in the Landau analysis of scattering amplitudes in particle physics. |
| title | Varieties of Lines in 3-Space |
| topic | Combinatorics High Energy Physics - Theory Commutative Algebra Algebraic Geometry 13P25, 14N20, 14N15, 14J81 |
| url | https://arxiv.org/abs/2511.21333 |