Local description of phylogenetic group-based models
Motivated by phylogenetics, our aim is to obtain a system of equations that de ne a phylogenetic variety on an open set containing the biologically meaningful points. In this paper we consider phylogenetic varieties de ned via group-based models. For any nite abelian group G, we provide an explicit...
| Authors: | ; ; |
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| Format: | Report |
| Publication date: | 2013 |
| Country: | España |
| Institution: | Universitat Politècnica de Catalunya (UPC) |
| Repository: | UPCommons. Portal del coneixement obert de la UPC |
| Language: | English |
| OAI Identifier: | oai:upcommons.upc.edu:2117/22383 |
| Online Access: | https://hdl.handle.net/2117/22383 |
| Access Level: | Open access |
| Keyword: | Phylogeny Algebra Group theory group-based model phylogenetic invariant toric variety Filogènia Àlgebra Grups, Teoria de Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra Àrees temàtiques de la UPC::Ciències de la salut |
| Summary: | Motivated by phylogenetics, our aim is to obtain a system of equations that de ne a phylogenetic variety on an open set containing the biologically meaningful points. In this paper we consider phylogenetic varieties de ned via group-based models. For any nite abelian group G, we provide an explicit construction of codimX phylogenetic invariants (polynomial equations) of degree at most jGj that de ne the variety X on a Zariski open set U. The set U contains all biologically meaningful points when G is the group of the Kimura 3-parameter model. In particular, our main result con rms [Mic12, Conjecture 7.9] and, on the set U, Conjectures 29 and 30 of [SS05]. |
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