Toric varieties in phylogenetics

Volume 511 / 2015

M. Michałek Dissertationes Mathematicae 511 (2015), 1-86 MSC: Primary 14M25, 13P25; Secondary 52B20. DOI: 10.4064/dm511-0-1


The paper contains a revised, and extended by new results, part of the author's PhD thesis. The main objects that we study are toric varieties naturally associated to special Markov processes on trees. Such Markov processes can be defined by a tree $T$ and a group $G$. They are called group-based models. The main, but not unique, motivation to consider these processes comes from phylogenetics. We study the geometry, defining equations and combinatorial description of the associated toric varieties. We obtain new results for a large class of not necessarily abelian group-based models, which we call $G$-models. We also prove that equations of degree $4$ define the projective scheme representing the $3$-Kimura model.


  • M. MichałekInstitute of Mathematics
    Polish Academy of Sciences
    Śniadeckich 8
    00-656 Warszawa, Poland
    Freie Universität Berlin
    Fachbereich Mathematik und Informatik
    Mathematisches Institut
    Arnimallee 3
    14195 Berlin, Germany

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