Parke-Taylor varieties
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915489817559040 |
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| author | Hollering, Benjamin Pavlov, Dmitrii |
| author_facet | Hollering, Benjamin Pavlov, Dmitrii |
| contents | Parke-Taylor functions are certain rational functions on the Grassmannian of lines encoding MHV amplitudes in particle physics. For $n$ particles there are $n!$ Parke-Taylor functions, corresponding to all orderings of the particles. Linear relations between these functions have been extensively studied in the last years. We here describe all non-linear polynomial relations between these functions in a simple combinatorial way and study the variety parametrized by them, called the Parke-Taylor variety. We show that the Parke-Taylor variety is linearly isomorphic to the log canonical embedding of the moduli space $\overline{\mathcal{M}}_{0,n}$ due to Keel and Tevelev, and that the intersection with the algebraic torus recovers the open part, $\mathcal{M}_{0,n}$. We give an explicit description of this isomorphism. Unlike the log canonical embedding, this Parke-Taylor embedding respects the symmetry of the $n$ marked points and is constructed in a single-step procedure, avoiding the intermediate embedding into a product of projective spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_09323 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Parke-Taylor varieties Hollering, Benjamin Pavlov, Dmitrii Algebraic Geometry High Energy Physics - Theory Commutative Algebra Combinatorics Parke-Taylor functions are certain rational functions on the Grassmannian of lines encoding MHV amplitudes in particle physics. For $n$ particles there are $n!$ Parke-Taylor functions, corresponding to all orderings of the particles. Linear relations between these functions have been extensively studied in the last years. We here describe all non-linear polynomial relations between these functions in a simple combinatorial way and study the variety parametrized by them, called the Parke-Taylor variety. We show that the Parke-Taylor variety is linearly isomorphic to the log canonical embedding of the moduli space $\overline{\mathcal{M}}_{0,n}$ due to Keel and Tevelev, and that the intersection with the algebraic torus recovers the open part, $\mathcal{M}_{0,n}$. We give an explicit description of this isomorphism. Unlike the log canonical embedding, this Parke-Taylor embedding respects the symmetry of the $n$ marked points and is constructed in a single-step procedure, avoiding the intermediate embedding into a product of projective spaces. |
| title | Parke-Taylor varieties |
| topic | Algebraic Geometry High Energy Physics - Theory Commutative Algebra Combinatorics |
| url | https://arxiv.org/abs/2509.09323 |