Phylogenetic toric varieties on graphs
Weronika Buczyńska
Department of Mathematics, Texas A\&M University, College Station, TX 77843, USA
DOI: 10.1007/s10801-011-0308-2
Abstract
We define phylogenetic projective toric model of a trivalent graph as a generalization of a binary symmetric model of a trivalent phylogenetic tree. Generators of the projective coordinate ring of the models of graphs with one cycle are explicitly described. The phylogenetic models of graphs with the same topological invariants are deformation-equivalent and share the same Hilbert function. We also provide an algorithm to compute the Hilbert function.
Pages: 421–460
Keywords: binary symmetric model; GIT quotient; Hilbert function
Full Text: PDF
References
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3. Buczyńska, W., Wiśniewski, J.A.: On geometry of binary symmetric models of phylogenetic trees. J. Eur. Math. Soc. 9(3), 609-635 (2007)
4. Eisenbud, D.: Commutative Algebra with a View Toward Algebraic Geometry. Graduate Texts in Mathematics, vol.
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6. Fulton, W.: Introduction to Toric Varieties. Annals of Mathematics Studies, vol.
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14. Miller, E., Sturmfels, B.: Combinatorial Commutative Algebra. Graduate Texts in Mathematics, vol.
227. Springer, New York (2005)
15. Oda, T.: Convex Bodies and Algebraic Geometry. Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol.
15. Springer, Berlin, (1988). An introduction to the theory of toric varieties, Translated from the Japanese
16. Pachter, L., Sturmfels, B.: Statistics. In: Algebraic Statistics for Computational Biology, pp. 3-42.
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